
@inproceedings{courty_domain_2014,
	title = {Domain {Adaptation} with {Regularized} {Optimal} {Transport}},
	booktitle = {Machine {Learning} and {Knowledge} {Discovery} in {Databases}},
	author = {Courty, Nicolas and Flamary, Rémi and Tuia, Devis},
	year = {2014},
	keywords = {Domain Adaptation, Regularization Term, Source Distribution, Target Distribution, Target Domain},
	pages = {274--289},
}

@inproceedings{yurochkin_hierarchical_2019,
	title = {Hierarchical {Optimal} {Transport} for {Document} {Representation}},
	abstract = {The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word mover's distance. 
We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.},
	booktitle = {Proceedings of the 33rd {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Yurochkin, Mikhail and Claici, Sebastian and Chien, Edward and Mirzazadeh, Farzaneh and Solomon, Justin M},
	year = {2019},
}

@inproceedings{xie_differentiable_2020,
	title = {Differentiable {Top}-k {Operator} with {Optimal} {Transport}},
	abstract = {The top-k operation, i.e., finding the k largest or smallest elements from a collection of scores, is an important model component, which is widely used in information retrieval, machine learning, and data mining. However, if the top-k operation is implemented in an algorithmic way, e.g., using bubble algorithm, the resulting model cannot be trained in an end-to-end way using prevalent gradient descent algorithms. This is because these implementations typically involve swapping indices, whose gradient cannot be computed. Moreover, the corresponding mapping from the input scores to the indicator vector of whether this element belongs to the top-k set is essentially discontinuous. To address the issue, we propose a smoothed approximation, namely the SOFT (Scalable Optimal transport-based diFferenTiable) top-k operator. Specifically, our SOFT top-k operator approximates the output of the top-k operation as the solution of an Entropic Optimal Transport (EOT) problem. The gradient of the SOFT operator can then be efficiently approximated based on the optimality conditions of EOT problem. We apply the proposed operator to the k-nearest neighbors and beam search algorithms, and demonstrate improved performance.},
	booktitle = {Proceedings of the 34th {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Xie, Yujia and Dai, Hanjun and Chen, Minshuo and Dai, Bo and Zhao, Tuo and Zha, Hongyuan and Wei, Wei and Pfister, Tomas},
	year = {2020},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

@inproceedings{wang_automatically_2020,
	title = {Automatically {Learning} {Compact} {Quality}-aware {Surrogates} for {Optimization} {Problems}},
	abstract = {Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space. Empirically, we demonstrate these improvements on a non-convex adversary modeling task, a submodular recommendation task and a convex portfolio optimization task.},
	booktitle = {Proceedings of the 34th {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Wang, Kai and Wilder, Bryan and Perrault, Andrew and Tambe, Milind},
	year = {2020},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, notion},
}

@book{villani_optimal_2008,
	address = {Berlin, Heidelberg},
	title = {Optimal {Transport}, {Old} and {New}},
	volume = {338},
	copyright = {http://www.springer.com/tdm},
	isbn = {978-3-540-71049-3},
	urldate = {2024-05-30},
	publisher = {Springer Science \& Business Media},
	author = {Villani, Cédric},
	editor = {Berger, M. and Eckmann, B. and De La Harpe, P. and Hirzebruch, F. and Hitchin, N. and Hörmander, L. and Kupiainen, A. and Lebeau, G. and Ratner, M. and Serre, D. and Sinai, Ya. G. and Sloane, N. J. A. and Vershik, A. M. and Waldschmidt, M.},
	year = {2008},
	keywords = {Monge-Kantorovich problem, Optimal transport, Riemannian geometry, curvature, dynamical systems, partial differential equations},
}

@inproceedings{verdu_total_2014,
	title = {Total {Variation} {Distance} and the {Distribution} of {Relative} {Information}},
	abstract = {We give explicit expressions, upper and lower bounds on the total variation distance between P and Q in terms of the distribution of the random variables log dP/dQ (X) and log dP/dQ(Y), where X and Y are distributed accorκding to P and Q respectively.},
	urldate = {2024-08-14},
	booktitle = {Information {Theory} and {Applications} {Workshop} ({ITA})},
	author = {Verdú, Sergio},
	year = {2014},
	keywords = {Entropy, Information theory, Q measurement, Random variables, US Government, Upper bound},
	pages = {1--3},
}

@inproceedings{tran_transferability_2019,
	title = {Transferability and {Hardness} of {Supervised} {Classification} {Tasks}},
	abstract = {We propose a novel approach for estimating the difﬁculty and transferability of supervised classiﬁcation tasks. Unlike previous work, our approach is solution agnostic and does not require or assume trained models. Instead, we estimate these values using an information theoretic approach: treating training labels as random variables and exploring their statistics. When transferring from a source to a target task, we consider the conditional entropy between two such variables (i.e., label assignments of the two tasks). We show analytically and empirically that this value is related to the loss of the transferred model. We further show how to use this value to estimate task hardness. We test our claims extensively on three large scale data sets—CelebA (40 tasks), Animals with Attributes 2 (85 tasks), and Caltech-UCSD Birds 200 (312 tasks)—together representing 437 classiﬁcation tasks. We provide results showing that our hardness and transferability estimates are strongly correlated with empirical hardness and transferability. As a case study, we transfer a learned face recognition model to CelebA attribute classiﬁcation tasks, showing state of the art accuracy for tasks estimated to be highly transferable.},
	booktitle = {Proceedings of the {IEEE}/{CVF} {International} {Conference} on {Computer} {Vision} ({ICCV})},
	author = {Tran, Anh and Nguyen, Cuong and Hassner, Tal},
	year = {2019},
}

@inproceedings{shui_principled_2019,
	title = {A {Principled} {Approach} for {Learning} {Task} {Similarity} in {Multitask} {Learning}},
	abstract = {Multitask learning aims at solving a set of related tasks simultaneously, by exploiting the shared knowledge for improving the performance on individual tasks. Hence, an important aspect of multitask learning is to understand the similarities within a set of tasks. Previous works have incorporated this similarity information explicitly (e.g., weighted loss for each task) or implicitly (e.g., adversarial loss for feature adaptation), to achieve good empirical performances. However, the theoretical motivations for adding task similarity knowledge are often missing or incomplete. In this paper, we give a different perspective from a theoretical point of view to understand this practice. We ﬁrst provide an upper bound on the generalization error of multitask learning, showing the beneﬁt of explicit and implicit task similarity knowledge. We systematically derive the bounds based on two distinct task similarity metrics: H divergence and Wasserstein distance. From these theoretical results, we revisit the Adversarial Multitask Neural Network, proposing a new training algorithm to learn the task relation coefﬁcients and neural network parameters iteratively. We assess our new algorithm empirically on several benchmarks, showing not only that we ﬁnd interesting and robust task relations, but that the proposed approach outperforms the baselines, reafﬁrming the beneﬁts of theoretical insight in algorithm design.},
	booktitle = {Proceedings of the {Twenty}-{Eighth} {International} {Joint} {Conference} on {Artificial} {Intelligence}},
	author = {Shui, Changjian and Abbasi, Mahdieh and Robitaille, Louis-Émile and Wang, Boyu and Gagné, Christian},
	year = {2019},
}

@inproceedings{shah_decision-focused_2022,
	title = {Decision-{Focused} {Learning} without {Differentiable} {Optimization}: {Learning} {Locally} {Optimized} {Decision} {Losses}},
	shorttitle = {Decision-{Focused} {Learning} without {Differentiable} {Optimization}},
	abstract = {Decision-Focused Learning (DFL) is a paradigm for tailoring a predictive model to a downstream optimization task that uses its predictions in order to perform better on that specific task. The main technical challenge associated with DFL is that it requires being able to differentiate through the optimization problem, which is difficult due to discontinuous solutions and other challenges. Past work has largely gotten around this issue by handcrafting task-specific surrogates to the original optimization problem that provide informative gradients when differentiated through. However, the need to handcraft surrogates for each new task limits the usability of DFL. In addition, there are often no guarantees about the convexity of the resulting surrogates and, as a result, training a predictive model using them can lead to inferior local optima. In this paper, we do away with surrogates altogether and instead learn loss functions that capture task-specific information. To the best of our knowledge, ours is the first approach that entirely replaces the optimization component of decision-focused learning with a loss that is automatically learned. Our approach (a) only requires access to a black-box oracle that can solve the optimization problem and is thus generalizable, and (b) can be convex by construction and so can be easily optimized over. We evaluate our approach on three resource allocation problems from the literature and find that our approach outperforms learning without taking into account task structure in all three domains, and even hand-crafted surrogates from the literature.},
	booktitle = {Proceedings of the 36th {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Shah, Sanket and Wang, Kai and Wilder, Bryan and Perrault, Andrew and Tambe, Milind},
	year = {2022},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, notion},
}

@misc{qi_integrated_2023,
	title = {Integrated {Conditional} {Estimation}-{Optimization}},
	doi = {10.48550/arXiv.2110.12351},
	abstract = {Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of uncertain parameters and then optimizing the objective based on the estimation, we propose an integrated conditional estimation-optimization (ICEO) framework that estimates the underlying conditional distribution of the random parameter while considering the structure of the optimization problem. We directly model the relationship between the conditional distribution of the random parameter and the contextual features, and then estimate the probabilistic model with an objective that aligns with the downstream optimization problem. We show that our ICEO approach is asymptotically consistent under moderate regularity conditions and further provide finite performance guarantees in the form of generalization bounds. Computationally, performing estimation with the ICEO approach is a non-convex and often non-differentiable optimization problem. We propose a general methodology for approximating the potentially non-differentiable mapping from estimated conditional distribution to the optimal decision by a differentiable function, which greatly improves the performance of gradient-based algorithms applied to the non-convex problem. We also provide a polynomial optimization solution approach in the semi-algebraic case. Numerical experiments are also conducted to show the empirical success of our approach in different situations including with limited data samples and model mismatches.},
	urldate = {2024-05-21},
	publisher = {arXiv},
	author = {Qi, Meng and Grigas, Paul and Shen, Zuo-Jun Max},
	year = {2023},
	note = {arXiv:2110.12351},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, notion},
}

@inproceedings{vlastelica_differentiation_2020,
	title = {Differentiation of {Blackbox} {Combinatorial} {Solvers}},
	abstract = {Achieving fusion of deep learning with combinatorial algorithms promises transformative changes to artificial intelligence. One possible approach is to introduce combinatorial building blocks into neural networks. Such end-to-end architectures have the potential to tackle combinatorial problems on raw input data such as ensuring global consistency in multi-object tracking or route planning on maps in robotics. In this work, we present a method that implements an efficient backward pass through blackbox implementations of combinatorial solvers with linear objective functions. We provide both theoretical and experimental backing. In particular, we incorporate the Gurobi MIP solver, Blossom V algorithm, and Dijkstra's algorithm into architectures that extract suitable features from raw inputs for the traveling salesman problem, the min-cost perfect matching problem and the shortest path problem.},
	urldate = {2024-04-22},
	booktitle = {Eighth {International} {Conference} on {Learning} {Representations}},
	author = {Vlastelica, Marin and Paulus, Anselm and Musil, Vit and Martius, Georg and Rolinek, Michal},
	year = {2020},
	keywords = {notion},
}

@article{muller_integral_1997,
	title = {Integral {Probability} {Metrics} and {Their} {Generating} {Classes} of {Functions}},
	volume = {29},
	issn = {0001-8678},
	abstract = {We consider probability metrics of the following type: for a class F of functions and probability measures P, Q we define \$d\_\{{\textbackslash}germ\{F\}\}(P,{\textbackslash} Q){\textbackslash}coloneq {\textbackslash}text\{sup\}\_\{f{\textbackslash}in {\textbackslash}germ\{F\}\}{\textbar}{\textbackslash}int f{\textbackslash},dP-{\textbackslash}int f{\textbackslash},dQ{\textbar}\$. A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.},
	number = {2},
	journal = {Advances in Applied Probability},
	author = {Müller, Alfred},
	year = {1997},
	pages = {429--443},
}

@article{memoli_gromovwasserstein_2011,
	title = {Gromov–{Wasserstein} {Distances} and the {Metric} {Approach} to {Object} {Matching}},
	volume = {11},
	issn = {1615-3383},
	abstract = {This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff distance which have the goal of modeling and tackling the practical problems of object matching and comparison. Objects are viewed as metric measure spaces, and based on ideas from mass transportation, a Gromov–Wasserstein type of distance between objects is defined. This reformulation yields a distance between objects which is more amenable to practical computations but retains all the desirable theoretical underpinnings. The theoretical properties of this new notion of distance are studied, and it is established that it provides a strict metric on the collection of isomorphism classes of metric measure spaces. Furthermore, the topology generated by this metric is studied, and sufficient conditions for the pre-compactness of families of metric measure spaces are identified. A second goal of this paper is to establish links to several other practical methods proposed in the literature for comparing/matching shapes in precise terms. This is done by proving explicit lower bounds for the proposed distance that involve many of the invariants previously reported by researchers. These lower bounds can be computed in polynomial time. The numerical implementations of the ideas are discussed and computational examples are presented.},
	number = {4},
	journal = {Foundations of Computational Mathematics},
	author = {Mémoli, Facundo},
	year = {2011},
	keywords = {53C23, 54E35, 60D05, 68T10, 68U05, Data analysis, Gromov–Hausdorff distances, Gromov–Wasserstein distances, Mass transport, Metric measure spaces, Shape matching},
	pages = {417--487},
}

@inproceedings{mercioni_survey_2019,
	title = {A {Survey} of {Distance} {Metrics} in {Clustering} {Data} {Mining} {Techniques}},
	abstract = {Lately, due to the increasing size of databases, several aspects have been studied in detail, such as grouping, searching for the closest neighbor and other identification methods. It has been found that in the multidimensional space, the concept of distance does not offer high performance. In this paper, we study the effect of different types of distances on the group to see the similarities between objects. Among these distances we mention two distances: the Euclidean distance and Manhattan distance, implemented in a system developed to identify the architectural styles of the buildings. The aim of this paper is using cluster analysis to identify distance metrics impact in detection of architectural styles using Data Mining techniques.},
	booktitle = {Proceedings of the 3rd {International} {Conference} on {Graphics} and {Signal} {Processing}},
	author = {Mercioni, Marina Adriana and Holban, Stefan},
	year = {2019},
}

@inproceedings{muzellec_generalizing_2018,
	title = {Generalizing {Point} {Embeddings} using the {Wasserstein} {Space} of {Elliptical} {Distributions}},
	abstract = {Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability distributions, namely distributions whose densities have elliptical level sets. We endow these measures with the 2-Wasserstein metric, with two important beneﬁts: (i) For such measures, the squared 2-Wasserstein metric has a closed form, equal to a weighted sum of the squared Euclidean distance between means and the squared Bures metric between covariance matrices. The latter is a Riemannian metric between positive semi-deﬁnite matrices, which turns out to be Euclidean on a suitable factor representation of such matrices, which is valid on the entire geodesic between these matrices. (ii) The 2-Wasserstein distance boils down to the usual Euclidean metric when comparing Diracs, and therefore provides a natural framework to extend point embeddings. We show that for these reasons Wasserstein elliptical embeddings are more intuitive and yield tools that are better behaved numerically than the alternative choice of Gaussian embeddings with the Kullback-Leibler divergence. In particular, and unlike previous work based on the KL geometry, we learn elliptical distributions that are not necessarily diagonal. We demonstrate the advantages of elliptical embeddings by using them for visualization, to compute embeddings of words, and to reﬂect entailment or hypernymy.},
	booktitle = {Proceedings of the 32nd {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Muzellec, Boris and Cuturi, Marco},
	year = {2018},
}

@article{kantorovitch_translocation_1942,
	title = {On the {Translocation} of {Masses}},
	volume = {37},
	issn = {0002-3264},
	number = {1},
	journal = {Dokl. Akad. Nauk SSSR},
	author = {Kantorovitch, L.},
	year = {1942},
	keywords = {notion},
	pages = {227--229},
}

@inproceedings{just_lava_2023,
	title = {{LAVA}: {Data} {Valuation} without {Pre}-{Specified} {Learning} {Algorithms}},
	abstract = {Traditionally, data valuation (DV) is posed as a problem of equitably splitting the validation performance of a learning algorithm among the training data. As a result, the calculated data values depend on many design choices of the underlying learning algorithm. However, this dependence is undesirable for many DV use cases, such as setting priorities over different data sources in a data acquisition process and informing pricing mechanisms in a data marketplace. In these scenarios, data needs to be valued before the actual analysis and the choice of the learning algorithm is still undetermined then. Another side-effect of the dependence is that to assess the value of individual points, one needs to re-run the learning algorithm with and without a point, which incurs a large computation burden. This work leapfrogs over the current limits of data valuation methods by introducing a new framework that can value training data in a way that is oblivious to the downstream learning algorithm. Our main results are as follows. (1) We develop a proxy for the validation performance associated with a training set based on a non-conventional class-wise Wasserstein distance between training and validation sets. We show that the distance characterizes the upper bound of the validation performance for any given model under certain Lipschitz conditions. (2) We develop a novel method to value individual data based on the sensitivity analysis of the class-wise Wasserstein distance. Importantly, these values can be directly obtained for free from the output of off-the-shelf optimization solvers when computing the distance. (3) We evaluate our new data valuation framework over various use cases related to detecting low-quality data and show that, surprisingly, the learning-agnostic feature of our framework enables a significant improvement over SOTA performance while being orders of magnitude faster.},
	booktitle = {International {Conference} on {Learning} {Representations}},
	author = {Just, Hoang Anh and Kang, Feiyang and Wang, Jiachen T. and Zeng, Yi and Ko, Myeongseob and Jin, Ming and Jia, Ruoxi},
	year = {2023},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@inproceedings{jiang_opendataval_2023,
	title = {{OpenDataVal}: a {Unified} {Benchmark} for {Data} {Valuation}},
	abstract = {Assessing the quality and impact of individual data points is critical for improving model performance and mitigating undesirable biases within the training dataset. Several data valuation algorithms have been proposed to quantify data quality, however, there lacks a systemic and standardized benchmarking system for data valuation. In this paper, we introduce OpenDataVal, an easy-to-use and unified benchmark framework that empowers researchers and practitioners to apply and compare various data valuation algorithms. OpenDataVal provides an integrated environment that includes (i) a diverse collection of image, natural language, and tabular datasets, (ii) implementations of eleven different state-of-the-art data valuation algorithms, and (iii) a prediction model API that can import any models in scikit-learn. Furthermore, we propose four downstream machine learning tasks for evaluating the quality of data values. We perform benchmarking analysis using OpenDataVal, quantifying and comparing the efficacy of state-of-the-art data valuation approaches. We find that no single algorithm performs uniformly best across all tasks, and an appropriate algorithm should be employed for a user’s downstream task. OpenDataVal is publicly available at https://opendataval.github.io with comprehensive documentation. Furthermore, we provide a leaderboard where researchers can evaluate the effectiveness of their own data valuation algorithms.},
	language = {en},
	booktitle = {Proceedings of the 37th {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Jiang, Kevin Fu and Zou, James and Liang, Weixin and Kwon, Yongchan},
	year = {2023},
}

@inproceedings{janati_wasserstein_2019,
	title = {Wasserstein {Regularization} for {Sparse} {Multi}-{Task} {Regression}},
	abstract = {We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-called multi-task techniques were proposed, which consist in the simultaneous estimation of several related models. Combined with sparsity assumptions, it lead to models enforcing the active regressors to be shared across models, thanks to, for instance L1/Lq norms. We argue in this paper that these techniques fail to leverage the spatial information associated to regressors. Indeed, while sparse priors enforce that only a small subset of variables is used, the assumption that these regressors overlap across all tasks is overly simplistic given the spatial variability observed in real data. In this paper, we propose a convex regularizer for multi-task regression that encodes a more flexible geometry. Our regularizer is based on unbalanced optimal transport (OT) theory, and can take into account a prior geometric knowledge on the regressor variables, without necessarily requiring overlapping supports. We derive an efficient algorithm based on a regularized formulation of OT, which iterates through applications of Sinkhorn’s algorithm along with coordinate descent iterations. The performance of our model is demonstrated on regular grids with both synthetic and real datasets as well as complex triangulated geometries of the cortex with an application in neuroimaging.},
	booktitle = {Proceedings of the {Twenty}-{Second} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	author = {Janati, Hicham and Cuturi, Marco and Gramfort, Alexandre},
	year = {2019},
}

@article{elmachtoub_smart_2022,
	title = {Smart “{Predict}, then {Optimize}”},
	volume = {68},
	abstract = {Many real-world analytics problems involve two significant challenges: prediction and optimization. Because of the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart “Predict, then Optimize” (SPO), which directly leverages the optimization problem structure—that is, its objective and constraints—for designing better prediction models. A key component of our framework is the SPO loss function, which measures the decision error induced by a prediction. Training a prediction model with respect to the SPO loss is computationally challenging, and, thus, we derive, using duality theory, a convex surrogate loss function, which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions. Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest-path and portfolio-optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular, when the prediction model being trained is misspecified. We find that linear models trained using SPO+ loss tend to dominate random-forest algorithms, even when the ground truth is highly nonlinear.
            This paper was accepted by Yinyu Ye, optimization.
            Supplemental Material: Data and the online appendix are available at https://doi.org/10.1287/mnsc.2020.3922},
	language = {en},
	number = {1},
	journal = {Management Science},
	author = {Elmachtoub, Adam N. and Grigas, Paul},
	year = {2022},
	keywords = {notion},
	pages = {9--26},
}

@inproceedings{donti_task-based_2017,
	title = {Task-based {End}-to-end {Model} {Learning} in {Stochastic} {Optimization}},
	abstract = {With the increasing popularity of machine learning techniques, it has become common to see prediction algorithms operating within some larger process. However, the criteria by which we train these algorithms often differ from the ultimate criteria on which we evaluate them. This paper proposes an end-to-end approach for learning probabilistic machine learning models in a manner that directly captures the ultimate task-based objective for which they will be used, within the context of stochastic programming. We present three experimental evaluations of the proposed approach: a classical inventory stock problem, a real-world electrical grid scheduling task, and a real-world energy storage arbitrage task. We show that the proposed approach can outperform both traditional modeling and purely black-box policy optimization approaches in these applications.},
	booktitle = {Proceedings of the 31st {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Donti, Priya and Amos, Brandon and Kolter, J. Zico},
	year = {2017},
	keywords = {notion},
}

@article{delon_wasserstein-type_2020,
	title = {A {Wasserstein}-{Type} {Distance} in the {Space} of {Gaussian} {Mixture} {Models}},
	volume = {13},
	abstract = {In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.},
	number = {2},
	urldate = {2024-05-31},
	journal = {SIAM Journal on Imaging Sciences},
	author = {Delon, Julie and Desolneux, Agnès},
	year = {2020},
	keywords = {62-07, 65K05, 65K10, 68Q25, 68R10, 68U05, 68U10, 90C05, Gaussian mixture model, Wasserstein distance, barycenter, image processing applications, multimarginal optimal transport, optimal transport},
	pages = {936--970},
}

@inproceedings{courty_joint_2017,
	title = {Joint {Distribution} {Optimal} {Transportation} for {Domain} {Adaptation}},
	abstract = {This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function \$f\$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linear transformation between the joint feature/label space distributions of the two domain \${\textbackslash}mathcal\{P\}\_s\$ and \${\textbackslash}mathcal\{P\}\_t\$. We propose a solution of this problem with optimal transport, that allows to recover an estimated target \${\textbackslash}mathcal\{P\}{\textasciicircum}f\_t=(X,f(X))\$ by optimizing simultaneously the optimal coupling and \$f\$. We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results.},
	booktitle = {Proceedings of the 31st {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Courty, Nicolas and Flamary, Rémi and Habrard, Amaury and Rakotomamonjy, Alain},
	year = {2017},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, notion},
}

@article{ben-david_theory_2010,
	title = {A {Theory} of {Learning} from {Different} {Domains}},
	volume = {79},
	journal = {Machine Learning},
	author = {Ben-David, Shai and Blitzer, John and Crammer, Koby and Kulesza, Alex and Pereira, Fernando and Vaughan, Jennifer Wortman},
	year = {2010},
	keywords = {Domain adaptation, Learning theory, Sample-selection bias, Transfer learning},
	pages = {151--175},
}

@inproceedings{bansal_taskmet_2023,
	title = {{TaskMet}: {Task}-{Driven} {Metric} {Learning} for {Model} {Learning}},
	abstract = {Deep learning models are often deployed in downstream tasks that the training procedure may not be aware of. For example, models solely trained to achieve accurate predictions may struggle to perform well on downstream tasks because seemingly small prediction errors may incur drastic task errors. The standard end-to-end learning approach is to make the task loss differentiable or to introduce a differentiable surrogate that the model can be trained on. In these settings, the task loss needs to be carefully balanced with the prediction loss because they may have conflicting objectives. We propose take the task loss signal one level deeper than the parameters of the model and use it to learn the parameters of the loss function the model is trained on, which can be done by learning a metric in the prediction space. This approach does not alter the optimal prediction model itself, but rather changes the model learning to emphasize the information important for the downstream task. This enables us to achieve the best of both worlds: a prediction model trained in the original prediction space while also being valuable for the desired downstream task. We validate our approach through experiments conducted in two main settings: 1) decision-focused model learning scenarios involving portfolio optimization and budget allocation, and 2) reinforcement learning in noisy environments with distracting states. The source code to reproduce our experiments is available at https://github.com/facebookresearch/taskmet},
	booktitle = {Proceedings of the 37th {International} {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Bansal, Dishank and Chen, Ricky T. Q. and Mukadam, Mustafa and Amos, Brandon},
	year = {2023},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Mathematics - Optimization and Control, Statistics - Machine Learning},
}

@inproceedings{amos_optnet_2017,
	title = {{OptNet}: {Differentiable} {Optimization} as a {Layer} in {Neural} {Networks}},
	shorttitle = {{OptNet}},
	abstract = {This paper presents OptNet, a network architecture that integrates optimization problems (here, specifically in the form of quadratic programs) as individual layers in larger end-to-end train-able deep networks. These layers encode constraints and complex dependencies between the hidden states that traditional convolutional and fully-connected layers often cannot capture. In this paper, we explore the foundations for such an architecture: we show how techniques from sensitivity analysis, bilevel optimization, and implicit differentiation can be used to exactly differentiate through these layers and with respect to layer parameters; we develop a highly efficient solver for these layers that exploits fast GPU-based batch solves within a primal-dual interior point method, and which provides backpropagation gradients with virtually no additional cost on top of the solve; and we highlight the application of these approaches in several problems. In one notable example, we show that the method is capable of learning to play mini-Sudoku (4x4) given just input and output games, with no a priori information about the rules of the game; this highlights the ability of our architecture to learn hard constraints better than other neural architectures.},
	booktitle = {Proceedings of the 34th {International} {Conference} on {Machine} {Learning}},
	author = {Amos, Brandon and Kolter, J. Zico},
	year = {2017},
	keywords = {notion},
}

@inproceedings{alvarez-melis_structured_2018,
	title = {Structured {Optimal} {Transport}},
	abstract = {Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation to sentence similarities or deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able to reflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties.  Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.},
	booktitle = {Proceedings of the {Twenty}-{First} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Alvarez-Melis, David and Jaakkola, Tommi and Jegelka, Stefanie},
	year = {2018},
}

@inproceedings{alvarez-melis_geometric_2020,
	title = {Geometric {Dataset} {Distances} via {Optimal} {Transport}},
	abstract = {The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameters (e.g., require training a model on each dataset). In this work we propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.},
	booktitle = {Proceedings of the 34th {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Alvarez-Melis, David and Fusi, Nicolo},
	year = {2020},
	keywords = {notion},
}

@inproceedings{mansour_domain_2009,
	title = {Domain {Adaptation}: {Learning} {Bounds} and {Algorithms}},
	abstract = {This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by Ben-David et al. (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive novel generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularization-based algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give novel algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.},
	booktitle = {Proceedings of {The} 22nd {Annual} {Conference} on {Learning} {Theory}},
	author = {Mansour, Yishay and Mohri, Mehryar and Rostamizadeh, Afshin},
	year = {2009},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
}

@misc{liu_active_2025,
	title = {Active {Learning} in the {Predict}-then-{Optimize} {Framework}: {A} {Margin}-{Based} {Approach}},
	shorttitle = {Active {Learning} in the {Predict}-then-{Optimize} {Framework}},
	abstract = {We develop the first active learning method in the predict-then-optimize framework. Specifically, we develop a learning method that sequentially decides whether to request the "labels" of feature samples from an unlabeled data stream, where the labels correspond to the parameters of an optimization model for decision-making. Our active learning method is the first to be directly informed by the decision error induced by the predicted parameters, which is referred to as the Smart Predict-then-Optimize (SPO) loss. Motivated by the structure of the SPO loss, our algorithm adopts a margin-based criterion utilizing the concept of distance to degeneracy and minimizes a tractable surrogate of the SPO loss on the collected data. In particular, we develop an efficient active learning algorithm with both hard and soft rejection variants, each with theoretical excess risk (i.e., generalization) guarantees. We further derive bounds on the label complexity, which refers to the number of samples whose labels are acquired to achieve a desired small level of SPO risk. Under some natural low-noise conditions, we show that these bounds can be better than the naive supervised learning approach that labels all samples. Furthermore, when using the SPO+ loss function, a specialized surrogate of the SPO loss, we derive a significantly smaller label complexity under separability conditions. We also present numerical evidence showing the practical value of our proposed algorithms in the settings of personalized pricing and the shortest path problem.},
	publisher = {arXiv},
	author = {Liu, Mo and Grigas, Paul and Liu, Heyuan and Shen, Zuo-Jun Max},
	year = {2025},
	note = {arXiv:2305.06584},
	keywords = {Computer Science - Machine Learning, Mathematics - Optimization and Control, Statistics - Machine Learning, notion},
}

@inproceedings{frogner_learning_2019,
	title = {Learning {Embeddings} into {Entropic} {Wasserstein} {Spaces}},
	abstract = {Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete probability distributions in a Wasserstein space, endowed with an optimal transport metric. Wasserstein spaces are much larger and more ﬂexible than Euclidean spaces, in that they can successfully embed a wider variety of metric structures. We exploit this ﬂexibility by learning an embedding that captures semantic information in the Wasserstein distance between embedded distributions. We examine empirically the representational capacity of our learned Wasserstein embeddings, showing that they can embed a wide variety of metric structures with smaller distortion than an equivalent Euclidean embedding. We also investigate an application to word embedding, demonstrating a unique advantage of Wasserstein embeddings: We can visualize the high-dimensional embedding directly, since it is a probability distribution on a low-dimensional space. This obviates the need for dimensionality reduction techniques like t-SNE for visualization.},
	booktitle = {International {Conference} on {Learning} {Representations}},
	author = {Frogner, Charlie and Mirzazadeh, Farzaneh and Solomon, Justin},
	year = {2019},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

@misc{elmachtoub_estimate-then-optimize_2025,
	title = {Estimate-{Then}-{Optimize} versus {Integrated}-{Estimation}-{Optimization} versus {Sample} {Average} {Approximation}: {A} {Stochastic} {Dominance} {Perspective}},
	shorttitle = {Estimate-{Then}-{Optimize} versus {Integrated}-{Estimation}-{Optimization} versus {Sample} {Average} {Approximation}},
	doi = {10.48550/arXiv.2304.06833},
	abstract = {In data-driven stochastic optimization, model parameters of the underlying distribution need to be estimated from data in addition to the optimization task. Recent literature considers integrating the estimation and optimization processes by selecting model parameters that lead to the best empirical objective performance. This integrated approach, which we call integrated-estimation-optimization (IEO), can be readily shown to outperform simple estimate-then-optimize (ETO) when the model is misspecified. In this paper, we show that a reverse behavior appears when the model class is well-specified and there is sufficient data. Specifically, for a general class of nonlinear stochastic optimization problems, we show that simple ETO outperforms IEO asymptotically when the model class covers the ground truth, in the strong sense of stochastic dominance of the regret. Namely, the entire distribution of the regret, not only its mean or other moments, is always better for ETO compared to IEO. Our results also apply to constrained, contextual optimization problems where the decision depends on observed features. Whenever applicable, we also demonstrate how standard sample average approximation (SAA) performs the worst when the model class is well-specified in terms of regret, and best when it is misspecified. Finally, we provide experimental results to support our theoretical comparisons and illustrate when our insights hold in finite-sample regimes and under various degrees of misspecification.},
	urldate = {2024-05-21},
	publisher = {arXiv},
	author = {Elmachtoub, Adam N. and Lam, Henry and Zhang, Haofeng and Zhao, Yunfan},
	year = {2025},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, Statistics - Methodology, notion},
}

@inproceedings{wilder_melding_2019,
	title = {Melding the {Data}-{Decisions} {Pipeline}: {Decision}-{Focused} {Learning} for {Combinatorial} {Optimization}},
	shorttitle = {Melding the {Data}-{Decisions} {Pipeline}},
	abstract = {Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating common classes of discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.},
	booktitle = {Proceedings of the {Thirty}-{Third} {AAAI} {Conference} on {Artificial} {Intelligence}},
	author = {Wilder, Bryan and Dilkina, Bistra and Tambe, Milind},
	year = {2019},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@misc{mandi_decision-focused_2022,
	title = {Decision-{Focused} {Learning}: {Through} the {Lens} of {Learning} to {Rank}},
	shorttitle = {Decision-{Focused} {Learning}},
	url = {http://arxiv.org/abs/2112.03609},
	doi = {10.48550/arXiv.2112.03609},
	abstract = {In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the objective function of a discrete combinatorial optimization problem for decision making. Decision-focused learning proposes to train the ML models, often neural network models, by directly optimizing the quality of decisions made by the optimization solvers. Based on a recent work that proposed a noise contrastive estimation loss over a subset of the solution space, we observe that decision-focused learning can more generally be seen as a learning-to-rank problem, where the goal is to learn an objective function that ranks the feasible points correctly. This observation is independent of the optimization method used and of the form of the objective function. We develop pointwise, pairwise and listwise ranking loss functions, which can be differentiated in closed form given a subset of solutions. We empirically investigate the quality of our generic methods compared to existing decision-focused learning approaches with competitive results. Furthermore, controlling the subset of solutions allows controlling the runtime considerably, with limited effect on regret.},
	urldate = {2025-04-08},
	publisher = {arXiv},
	author = {Mandi, Jayanta and Bucarey, Víctor and Mulamba, Maxime and Guns, Tias},
	month = jun,
	year = {2022},
	note = {arXiv:2112.03609 [cs]},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
}

@inproceedings{johnson-yu_characterizing_2023,
	title = {Characterizing and {Improving} the {Robustness} of {Predict}-{Then}-{Optimize} {Frameworks}},
	abstract = {Optimization tasks situated in incomplete information settings are often preceded by a prediction problem to estimate the missing information; past work shows the traditional predict-then-optimize (PTO) framework can be improved by training a predictive model with respect to the optimization task through a PTO paradigm called decision-focused learning. Little is known, however, about the performance of traditional PTO and decision-focused learning when exposed to adversarial label drift. We provide modifications of traditional PTO and decision-focused learning that attempt to improve robustness by anticipating label drift. When the predictive model is perfectly expressive, we cast these learning problems as Stackelberg games. With these games, we provide a necessary condition for when anticipating label drift can improve the performance of a PTO algorithm: if performance can be improved, then the downstream optimization objective must be asymmetric. We then bound the loss of decision quality in the presence of adversarial label drift to show there may exist a strict gap between the performance of the two algorithms. We verify our theoretical findings empirically in two asymmetric and two symmetric settings. These experimental results demonstrate that robustified decision-focused learning is generally more robust to adversarial label drift than both robust and traditional PTO.},
	booktitle = {Decision and {Game} {Theory} for {Security}},
	author = {Johnson-Yu, Sonja and Finocchiaro, Jessie and Wang, Kai and Vorobeychik, Yevgeniy and Sinha, Arunesh and Taneja, Aparna and Tambe, Milind},
	year = {2023},
	keywords = {notion},
}

@article{massey_kolmogorov-smirnov_1951,
	title = {The {Kolmogorov}-{Smirnov} {Test} for {Goodness} of {Fit}},
	volume = {46},
	language = {en},
	number = {253},
	journal = {Journal of the American Statistical Association},
	author = {Massey, Frank J.},
	month = mar,
	year = {1951},
	pages = {68--78},
}

@inproceedings{ren_decision-focused_2024,
	title = {Decision-{Focused} {Evaluation} of {Worst}-{Case} {Distribution} {Shift}},
	abstract = {Recent studies have shown that performance on downstream optimization tasks often diverges from standard accuracy-based losses, highlighting that the loss function of a predictive model should align with the decision task of the downstream optimizer. Despite this observation, no work\{—\} to our knowledge\{—\}has yet examined the impact of this divergence for distribution shift. In this paper, we demonstrate that worst-case distribution shifts identified by traditional average accuracy-based metrics fundamentally differ from those for the downstream decision task at hand. We introduce a novel framework that employs a hierarchical model structure to identify worst-case distribution shifts in predictive resource allocation settings. This task is more difficult than in standard distribution shift settings because of combinatorial interactions, where decisions depend on the joint presence of individuals in the allocation task. We show that the problem can be reformulated as a submodular optimization problem, enabling efficient approximations, to capture shifts both within and across instances of the optimization problem.},
	language = {en},
	booktitle = {Proceedings of the {Fortieth} {Conference} on {Uncertainty} in {Artificial} {Intelligence}},
	publisher = {PMLR},
	author = {Ren, Kevin and Byun, Yewon and Wilder, Bryan},
	year = {2024},
	pages = {3076--3093},
}

@inproceedings{redko_optimal_2019,
	title = {Optimal {Transport} for {Multi}-source {Domain} {Adaptation} under {Target} {Shift}},
	abstract = {In this paper, we tackle the problem of reducing discrepancies between multiple domains, i.e. multi-source domain adaptation, and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with different labels proportions. This problem, generally ignored in the vast majority of domain adaptation papers, is nevertheless critical in real-world applications, and we theoretically show its impact on the success of the adaptation. Our proposed method is based on optimal transport, a theory that has been successfully used to tackle adaptation problems in machine learning. The introduced approach, Joint Class Proportion and Optimal Transport (JCPOT), performs multi-source adaptation and target shift correction simultaneously by learning the class probabilities of the unlabeled target sample and the coupling allowing to align two (or more) probability distributions. Experiments on both synthetic and real-world data (satellite image pixel classification) task show the superiority of the proposed method over the state-of-the-art.},
	booktitle = {Proceedings of the {Twenty}-{Second} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Redko, Ievgen and Courty, Nicolas and Flamary, Rémi and Tuia, Devis},
	month = apr,
	year = {2019},
	pages = {849--858},
}

@inproceedings{zhang_domain_2013,
	series = {{ICML}'13},
	title = {Domain adaptation under target and conditional shift},
	abstract = {Let X denote the feature and Y the target. We consider domain adaptation under three possible scenarios: (1) the marginal PY changes, while the conditional PX/Y stays the same (target shift), (2) the marginal PY is fixed, while the conditional PX/Y changes with certain constraints (conditional shift), and (3) the marginal PY changes, and the conditional PX/Y changes with constraints (generalized target shift). Using background knowledge, causal interpretations allow us to determine the correct situation for a problem at hand. We exploit importance reweighting or sample transformation to find the learning machine that works well on test data, and propose to estimate the weights or transformations by reweighting or transforming training data to reproduce the covariate distribution on the test domain. Thanks to kernel embedding of conditional as well as marginal distributions, the proposed approaches avoid distribution estimation, and are applicable for high-dimensional problems. Numerical evaluations on synthetic and real-world data sets demonstrate the effectiveness of the proposed framework.},
	booktitle = {Proceedings of the 30th {International} {Conference} on {International} {Conference} on {Machine} {Learning}},
	author = {Zhang, Kun and Schölkopf, Bernhard and Muandet, Krikamol and Wang, Zhikun},
	year = {2013},
}

@misc{tang_pyepo_2023,
	title = {{PyEPO}: {A} {PyTorch}-based {End}-to-{End} {Predict}-then-{Optimize} {Library} for {Linear} and {Integer} {Programming}},
	shorttitle = {{PyEPO}},
	abstract = {In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this work, we present the PyEPO package, a PyTorchbased end-to-end predict-then-optimize library in Python. To the best of our knowledge, PyEPO (pronounced like pineapple with a silent "n") is the first such generic tool for linear and integer programming with predicted objective function coefficients. It provides four base algorithms: a convex surrogate loss function from the seminal work of Elmachtoub and Grigas [16], a differentiable black-box solver approach of Pogancic et al. [35], and two differentiable perturbation-based methods from Berthet et al. [6]. PyEPO provides a simple interface for the definition of new optimization problems, the implementation of state-of-the-art predict-then-optimize training algorithms, the use of custom neural network architectures, and the comparison of end-to-end approaches with the two-stage approach. PyEPO enables us to conduct a comprehensive set of experiments comparing a number of end-to-end and two-stage approaches along axes such as prediction accuracy, decision quality, and running time on problems such as Shortest Path, Multiple Knapsack, and the Traveling Salesperson Problem. We discuss some empirical insights from these experiments, which could guide future research. PyEPO and its documentation are available at https://github.com/khalil-research/PyEPO.},
	urldate = {2023-11-07},
	publisher = {arXiv},
	author = {Tang, Bo and Khalil, Elias B.},
	month = apr,
	year = {2023},
	note = {arXiv:2206.14234},
	keywords = {Computer Science - Machine Learning, Mathematics - Optimization and Control, notion},
}

@misc{sotiropoulou_strongly_2024,
	title = {Strongly {Isomorphic} {Neural} {Optimal} {Transport} {Across} {Incomparable} {Spaces}},
	url = {http://arxiv.org/abs/2407.14957},
	abstract = {Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming the same space for both distributions. However, the setting across ``incomparable spaces'' (e.g., of different dimensionality), corresponding to the Gromov- Wasserstein distance, remains underexplored, with existing methods often imposing restrictive assumptions on the cost function. In this paper, we present a novel neural formulation of the Gromov-Monge (GM) problem rooted in one of its fundamental properties: invariance to strong isomorphisms. We operationalize this property by decomposing the learnable OT map into two components: (i) an approximate strong isomorphism between the source distribution and an intermediate reference distribution, and (ii) a GM-optimal map between this reference and the target distribution. Our formulation leverages and extends the Monge gap regularizer of Uscidda \& Cuturi (2023) to eliminate the need for complex architectural requirements of other neural OT methods, yielding a simple but practical method that enjoys favorable theoretical guarantees. Our preliminary empirical results show that our framework provides a promising approach to learn OT maps across diverse spaces.},
	urldate = {2024-08-08},
	publisher = {arXiv},
	author = {Sotiropoulou, Athina and Alvarez-Melis, David},
	month = jul,
	year = {2024},
	note = {arXiv:2407.14957},
	keywords = {Computer Science - Machine Learning},
}

@misc{mandi_smart_2019,
	title = {Smart {Predict}-and-{Optimize} for {Hard} {Combinatorial} {Optimization} {Problems}},
	abstract = {Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estimation. Recently, Smart Predict and Optimize (SPO) has been proposed for problems with a linear objective function over the predictions, more specifically linear programming problems. It takes the regret of the predictions on the linear problem into account, by repeatedly solving it during learning. We investigate the use of SPO to solve more realistic discrete optimization problems. The main challenge is the repeated solving of the optimization problem. To this end, we investigate ways to relax the problem as well as warmstarting the learning and the solving. Our results show that even for discrete problems it often suffices to train by solving the relaxation in the SPO loss. Furthermore, this approach outperforms, for most instances, the state-of-the-art approach of Wilder, Dilkina, and Tambe. We experiment with weighted knapsack problems as well as complex scheduling problems and show for the first time that a predict-and-optimize approach can successfully be used on large-scale combinatorial optimization problems.},
	urldate = {2024-02-21},
	publisher = {arXiv},
	author = {Mandi, Jaynta and Demirović, Emir and Stuckey, Peter J. and Guns, Tias},
	month = nov,
	year = {2019},
	note = {arXiv:1911.10092},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Mathematics - Optimization and Control},
}

@misc{lawless_note_2022,
	title = {A {Note} on {Task}-{Aware} {Loss} via {Reweighing} {Prediction} {Loss} by {Decision}-{Regret}},
	url = {http://arxiv.org/abs/2211.05116},
	abstract = {In this short technical note we propose a baseline for decision-aware learning for contextual linear optimization, which solves stochastic linear optimization when cost coefficients can be predicted based on context information. We propose a decision-aware version of predict-then-optimize. We reweigh the prediction error by the decision regret incurred by an (unweighted) pilot estimator of costs to obtain a decision-aware predictor, then optimize with cost predictions from the decision-aware predictor. This method can be motivated as a finite-difference, iterate-independent approximation of the gradients of previously proposed end-to-end learning algorithms; it is also consistent with previously suggested intuition for end-to-end learning. This baseline is computationally easy to implement with readily available reweighted prediction oracles and linear optimization, and can be implemented with convex optimization so long as the prediction error minimization is convex. Empirically, we demonstrate that this approach can lead to improvements over a "predict-then-optimize" framework for settings with misspecified models, and is competitive with other end-to-end approaches. Therefore, due to its simplicity and ease of use, we suggest it as a simple baseline for end-to-end and decision-aware learning.},
	urldate = {2024-01-23},
	publisher = {arXiv},
	author = {Lawless, Connor and Zhou, Angela},
	month = nov,
	year = {2022},
	note = {arXiv:2211.05116},
	keywords = {Computer Science - Machine Learning, Mathematics - Optimization and Control, Statistics - Machine Learning},
}

@misc{kwon_data-oob_2023,
	title = {Data-{OOB}: {Out}-of-bag {Estimate} as a {Simple} and {Efficient} {Data} {Value}},
	shorttitle = {Data-{OOB}},
	url = {http://arxiv.org/abs/2304.07718},
	abstract = {Data valuation is a powerful framework for providing statistical insights into which data are beneficial or detrimental to model training. Many Shapley-based data valuation methods have shown promising results in various downstream tasks, however, they are well known to be computationally challenging as it requires training a large number of models. As a result, it has been recognized as infeasible to apply to large datasets. To address this issue, we propose Data-OOB, a new data valuation method for a bagging model that utilizes the out-of-bag estimate. The proposed method is computationally efficient and can scale to millions of data by reusing trained weak learners. Specifically, Data-OOB takes less than 2.25 hours on a single CPU processor when there are \$10{\textasciicircum}6\$ samples to evaluate and the input dimension is 100. Furthermore, Data-OOB has solid theoretical interpretations in that it identifies the same important data point as the infinitesimal jackknife influence function when two different points are compared. We conduct comprehensive experiments using 12 classification datasets, each with thousands of sample sizes. We demonstrate that the proposed method significantly outperforms existing state-of-the-art data valuation methods in identifying mislabeled data and finding a set of helpful (or harmful) data points, highlighting the potential for applying data values in real-world applications.},
	urldate = {2023-11-07},
	publisher = {arXiv},
	author = {Kwon, Yongchan and Zou, James},
	month = jun,
	year = {2023},
	note = {arXiv:2304.07718},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

@misc{koh_understanding_2020,
	title = {Understanding {Black}-box {Predictions} via {Influence} {Functions}},
	url = {http://arxiv.org/abs/1703.04730},
	abstract = {How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data, thereby identifying training points most responsible for a given prediction. To scale up influence functions to modern machine learning settings, we develop a simple, efficient implementation that requires only oracle access to gradients and Hessian-vector products. We show that even on non-convex and non-differentiable models where the theory breaks down, approximations to influence functions can still provide valuable information. On linear models and convolutional neural networks, we demonstrate that influence functions are useful for multiple purposes: understanding model behavior, debugging models, detecting dataset errors, and even creating visually-indistinguishable training-set attacks.},
	urldate = {2024-01-17},
	publisher = {arXiv},
	author = {Koh, Pang Wei and Liang, Percy},
	month = dec,
	year = {2020},
	note = {arXiv:1703.04730},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@misc{guerdan_predictive_2024,
	title = {Predictive {Performance} {Comparison} of {Decision} {Policies} {Under} {Confounding}},
	url = {http://arxiv.org/abs/2404.00848},
	abstract = {Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing decision-making policy that is generally under-specified and dependent on unobservable factors. These sources of uncertainty are often addressed in practice by making strong assumptions about the data-generating mechanism. In this work, we propose a method to compare the predictive performance of decision policies under a variety of modern identification approaches from the causal inference and off-policy evaluation literatures (e.g., instrumental variable, marginal sensitivity model, proximal variable). Key to our method is the insight that there are regions of uncertainty that we can safely ignore in the policy comparison. We develop a practical approach for finite-sample estimation of regret intervals under no assumptions on the parametric form of the status quo policy. We verify our framework theoretically and via synthetic data experiments. We conclude with a real-world application using our framework to support a pre-deployment evaluation of a proposed modification to a healthcare enrollment policy.},
	urldate = {2024-07-29},
	publisher = {arXiv},
	author = {Guerdan, Luke and Coston, Amanda and Holstein, Kenneth and Wu, Zhiwei Steven},
	month = jun,
	year = {2024},
	note = {arXiv:2404.00848},
	keywords = {Computer Science - Computers and Society, Computer Science - Machine Learning, Statistics - Methodology},
}

@misc{ghorbani_data_2021,
	title = {Data {Shapley} {Valuation} for {Efficient} {Batch} {Active} {Learning}},
	url = {http://arxiv.org/abs/2104.08312},
	abstract = {Annotating the right set of data amongst all available data points is a key challenge in many machine learning applications. Batch active learning is a popular approach to address this, in which batches of unlabeled data points are selected for annotation, while an underlying learning algorithm gets subsequently updated. Increasingly larger batches are particularly appealing in settings where data can be annotated in parallel, and model training is computationally expensive. A key challenge here is scale - typical active learning methods rely on diversity techniques, which select a diverse set of data points to annotate, from an unlabeled pool. In this work, we introduce Active Data Shapley (ADS) -- a filtering layer for batch active learning that significantly increases the efficiency of active learning by pre-selecting, using a linear time computation, the highest-value points from an unlabeled dataset. Using the notion of the Shapley value of data, our method estimates the value of unlabeled data points with regards to the prediction task at hand. We show that ADS is particularly effective when the pool of unlabeled data exhibits real-world caveats: noise, heterogeneity, and domain shift. We run experiments demonstrating that when ADS is used to pre-select the highest-ranking portion of an unlabeled dataset, the efficiency of state-of-the-art batch active learning methods increases by an average factor of 6x, while preserving performance effectiveness.},
	urldate = {2023-11-02},
	publisher = {arXiv},
	author = {Ghorbani, Amirata and Zou, James and Esteva, Andre},
	month = apr,
	year = {2021},
	note = {arXiv:2104.08312},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

@article{courty_optimal_2017,
	title = {Optimal {Transport} for {Domain} {Adaptation}},
	volume = {39},
	copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
	issn = {0162-8828, 2160-9292},
	doi = {10.1109/TPAMI.2016.2615921},
	number = {9},
	urldate = {2024-08-02},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	author = {Courty, Nicolas and Flamary, Remi and Tuia, Devis and Rakotomamonjy, Alain},
	month = sep,
	year = {2017},
	pages = {1853--1865},
}

@article{cacciarelli_active_2023,
	title = {Active learning for data streams: a survey},
	issn = {0885-6125, 1573-0565},
	shorttitle = {Active learning for data streams},
	doi = {10.1007/s10994-023-06454-2},
	abstract = {Online active learning is a paradigm in machine learning that aims to select the most informative data points to label from a data stream. The problem of minimizing the cost associated with collecting labeled observations has gained a lot of attention in recent years, particularly in real-world applications where data is only available in an unlabeled form. Annotating each observation can be time-consuming and costly, making it difficult to obtain large amounts of labeled data. To overcome this issue, many active learning strategies have been proposed in the last decades, aiming to select the most informative observations for labeling in order to improve the performance of machine learning models. These approaches can be broadly divided into two categories: static pool-based and stream-based active learning. Pool-based active learning involves selecting a subset of observations from a closed pool of unlabeled data, and it has been the focus of many surveys and literature reviews. However, the growing availability of data streams has led to an increase in the number of approaches that focus on online active learning, which involves continuously selecting and labeling observations as they arrive in a stream. This work aims to provide an overview of the most recently proposed approaches for selecting the most informative observations from data streams in real time. We review the various techniques that have been proposed and discuss their strengths and limitations, as well as the challenges and opportunities that exist in this area of research.},
	urldate = {2023-12-20},
	journal = {Machine Learning},
	author = {Cacciarelli, Davide and Kulahci, Murat},
	month = nov,
	year = {2023},
	note = {arXiv:2302.08893},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, Statistics - Methodology},
}

@inproceedings{shah_leaving_2023,
	title = {Leaving the {Nest}: {Going} {Beyond} {Local} {Loss} {Functions} for {Predict}-{Then}-{Optimize}},
	shorttitle = {Leaving the {Nest}},
	abstract = {Predict-then-Optimize is a framework for using machine learning to perform decision-making under uncertainty. The central research question it asks is, "How can the structure of a decision-making task be used to tailor ML models for that specific task?" To this end, recent work has proposed learning task-specific loss functions that capture this underlying structure. However, current approaches make restrictive assumptions about the form of these losses and their impact on ML model behavior. These assumptions both lead to approaches with high computational cost, and when they are violated in practice, poor performance. In this paper, we propose solutions to these issues, avoiding the aforementioned assumptions and utilizing the ML model's features to increase the sample efficiency of learning loss functions. We empirically show that our method achieves state-of-the-art results in four domains from the literature, often requiring an order of magnitude fewer samples than comparable methods from past work. Moreover, our approach outperforms the best existing method by nearly 200\% when the localness assumption is broken.},
	booktitle = {Proceedings of the {AAAI} {Conference} on {Artificial} {Intelligence}},
	author = {Shah, Sanket and Perrault, Andrew and Wilder, Bryan and Tambe, Milind},
	year = {2023},
	keywords = {Artificial Intelligence (cs.AI), Decision-Focused Learning, FOS: Computer and information sciences, Machine Learning (cs.LG), notion},
}

@article{pearson_criterion_1900,
	title = {On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling},
	volume = {50},
	issn = {1941-5982, 1941-5990},
	language = {en},
	number = {302},
	urldate = {2024-08-08},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Pearson, Karl},
	month = jul,
	year = {1900},
	pages = {157--175},
}

@inproceedings{dwivedi_representation_2019,
	address = {Long Beach, CA, USA},
	title = {Representation {Similarity} {Analysis} for {Efficient} {Task} {Taxonomy} \& {Transfer} {Learning}},
	copyright = {https://doi.org/10.15223/policy-029},
	isbn = {978-1-72813-293-8},
	url = {https://ieeexplore.ieee.org/document/8953963/},
	doi = {10.1109/CVPR.2019.01267},
	abstract = {Transfer learning is widely used in deep neural network models when there are few labeled examples available. The common approach is to take a pre-trained network in a similar task and ﬁnetune the model parameters. This is usually done blindly without a pre-selection from a set of pretrained models, or by ﬁnetuning a set of models trained on different tasks and selecting the best performing one by cross-validation. We address this problem by proposing an approach to assess the relationship between visual tasks and their task-speciﬁc models. Our method uses Representation Similarity Analysis (RSA), which is commonly used to ﬁnd a correlation between neuronal responses from brain data and models. With RSA we obtain a similarity score among tasks by computing correlations between models trained on different tasks. Our method is efﬁcient as it requires only pre-trained models, and a few images with no further training. We demonstrate the effectiveness and efﬁciency of our method for generating task taxonomy on Taskonomy dataset. We next evaluate the relationship of RSA with the transfer learning performance on Taskonomy tasks and a new task: Pascal VOC semantic segmentation. Our results reveal that models trained on tasks with higher similarity score show higher transfer learning performance. Surprisingly, the best transfer learning result for Pascal VOC semantic segmentation is not obtained from the pre-trained model on semantic segmentation, probably due to the domain differences, and our method successfully selects the high performing models.},
	language = {en},
	urldate = {2024-08-12},
	booktitle = {2019 {IEEE}/{CVF} {Conference} on {Computer} {Vision} and {Pattern} {Recognition} ({CVPR})},
	publisher = {IEEE},
	author = {Dwivedi, Kshitij and Roig, Gemma},
	month = jun,
	year = {2019},
	pages = {12379--12388},
}

@article{japkowicz_class_2002,
	title = {The class imbalance problem: {A} systematic study},
	volume = {6},
	issn = {1088-467X},
	shorttitle = {The class imbalance problem},
	abstract = {In machine learning problems, differences in prior class probabilities -- or class imbalances -- have been reported to hinder the performance of some standard classifiers, such as decision trees. This paper presents a systematic study aimed at answering three different questions. First, we attempt to understand the nature of the class imbalance problem by establishing a relationship between concept complexity, size of the training set and class imbalance level. Second, we discuss several basic re-sampling or cost-modifying methods previously proposed to deal with the class imbalance problem and compare their effectiveness. The results obtained by such methods on artificial domains are linked to results in real-world domains. Finally, we investigate the assumption that the class imbalance problem does not only affect decision tree systems but also affects other classification systems such as Neural Networks and Support Vector Machines.},
	number = {5},
	journal = {Intell. Data Anal.},
	author = {Japkowicz, Nathalie and Stephen, Shaju},
	month = oct,
	year = {2002},
	pages = {429--449},
}

@inproceedings{zharmagambetov_landscape_2023,
	title = {Landscape {Surrogate}: {Learning} {Decision} {Losses} for {Mathematical} {Optimization} {Under} {Partial} {Information}},
	shorttitle = {Landscape {Surrogate}},
	abstract = {Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer \${\textbackslash}mathbf\{g\}\$ to tackle these challenging problems with \$f\$ as the objective, the optimization process can be substantially accelerated by leveraging past experience. The optimizer can be trained with supervision from known optimal solutions or implicitly by optimizing the compound function \$f{\textbackslash}circ {\textbackslash}mathbf\{g\}\$. The implicit approach may not require optimal solutions as labels and is capable of handling problem uncertainty; however, it is slow to train and deploy due to frequent calls to optimizer \${\textbackslash}mathbf\{g\}\$ during both training and testing. The training is further challenged by sparse gradients of \${\textbackslash}mathbf\{g\}\$, especially for combinatorial solvers. To address these challenges, we propose using a smooth and learnable Landscape Surrogate \$M\$ as a replacement for \$f{\textbackslash}circ {\textbackslash}mathbf\{g\}\$. This surrogate, learnable by neural networks, can be computed faster than the solver \${\textbackslash}mathbf\{g\}\$, provides dense and smooth gradients during training, can generalize to unseen optimization problems, and is efficiently learned via alternating optimization. We test our approach on both synthetic problems, including shortest path and multidimensional knapsack, and real-world problems such as portfolio optimization, achieving comparable or superior objective values compared to state-of-the-art baselines while reducing the number of calls to \${\textbackslash}mathbf\{g\}\$. Notably, our approach outperforms existing methods for computationally expensive high-dimensional problems.},
	urldate = {2024-01-22},
	booktitle = {{NeurIPS} 23},
	publisher = {arXiv},
	author = {Zharmagambetov, Arman and Amos, Brandon and Ferber, Aaron and Huang, Taoan and Dilkina, Bistra and Tian, Yuandong},
	year = {2023},
	note = {arXiv:2307.08964 [cs]},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
}

@inproceedings{zhang_rim_2021,
	title = {{RIM}: {Reliable} {Influence}-based {Active} {Learning} on {Graphs}},
	shorttitle = {{RIM}},
	abstract = {Message passing is the core of most graph models such as Graph Convolutional Network (GCN) and Label Propagation (LP), which usually require a large number of clean labeled data to smooth out the neighborhood over the graph. However, the labeling process can be tedious, costly, and error-prone in practice. In this paper, we propose to unify active learning (AL) and message passing towards minimizing labeling costs, e.g., making use of few and unreliable labels that can be obtained cheaply. We make two contributions towards that end. First, we open up a perspective by drawing a connection between AL enforcing message passing and social influence maximization, ensuring that the selected samples effectively improve the model performance. Second, we propose an extension to the influence model that incorporates an explicit quality factor to model label noise. In this way, we derive a fundamentally new AL selection criterion for GCN and LP--reliable influence maximization (RIM)--by considering quantity and quality of influence simultaneously. Empirical studies on public datasets show that RIM significantly outperforms current AL methods in terms of accuracy and efficiency.},
	urldate = {2024-01-23},
	booktitle = {35th {Conference} on {Neural} {Information} {Processing} {Systems} ({NeurIPS} 2021)},
	publisher = {arXiv},
	author = {Zhang, Wentao and Wang, Yexin and You, Zhenbang and Cao, Meng and Huang, Ping and Shan, Jiulong and Yang, Zhi and Cui, Bin},
	month = oct,
	year = {2021},
	note = {arXiv:2110.14854 [cs]},
	keywords = {Computer Science - Machine Learning},
}

@inproceedings{yoo_learning_2019,
	address = {Long Beach, CA, USA},
	title = {Learning {Loss} for {Active} {Learning}},
	isbn = {978-1-72813-293-8},
	doi = {10.1109/CVPR.2019.00018},
	urldate = {2024-01-23},
	booktitle = {2019 {IEEE}/{CVF} {Conference} on {Computer} {Vision} and {Pattern} {Recognition} ({CVPR})},
	publisher = {IEEE},
	author = {Yoo, Donggeun and Kweon, In So},
	month = jun,
	year = {2019},
	pages = {93--102},
}

@article{xia_reliable_2023,
	title = {Reliable {Active} {Learning} via {Influence} {Functions}},
	issn = {2835-8856},
	author = {Xia, Meng and Henao, Ricardo},
	year = {2023},
}

@misc{wang_scalable_2023,
	title = {Scalable {Decision}-{Focused} {Learning} in {Restless} {Multi}-{Armed} {Bandits} with {Application} to {Maternal} and {Child} {Health}},
	abstract = {This paper studies restless multi-armed bandit (RMAB) problems with unknown arm transition dynamics but with known correlated arm features. The goal is to learn a model to predict transition dynamics given features, where the Whittle index policy solves the RMAB problems using predicted transitions. However, prior works often learn the model by maximizing the predictive accuracy instead of final RMAB solution quality, causing a mismatch between training and evaluation objectives. To address this shortcoming, we propose a novel approach for decision-focused learning in RMAB that directly trains the predictive model to maximize the Whittle index solution quality. We present three key contributions: (i) we establish differentiability of the Whittle index policy to support decision-focused learning; (ii) we significantly improve the scalability of decision-focused learning approaches in sequential problems, specifically RMAB problems; (iii) we apply our algorithm to a previously collected dataset of maternal and child health to demonstrate its performance. Indeed, our algorithm is the first for decision-focused learning in RMAB that scales to real-world problem sizes.},
	urldate = {2023-11-27},
	publisher = {arXiv},
	author = {Wang, Kai and Verma, Shresth and Mate, Aditya and Shah, Sanket and Taneja, Aparna and Madhiwalla, Neha and Hegde, Aparna and Tambe, Milind},
	month = aug,
	year = {2023},
	note = {arXiv:2202.00916 [cs]},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
}

@article{ghorbani_data_2019,
	title = {Data {Shapley}: {Equitable} {Valuation} of {Data} for {Machine} {Learning}},
	shorttitle = {Data {Shapley}},
	abstract = {As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been suggested that individuals should be compensated for the data that they generate, but it is not clear what is an equitable valuation for individual data. In this work, we develop a principled framework to address data valuation in the context of supervised machine learning. Given a learning algorithm trained on \$n\$ data points to produce a predictor, we propose data Shapley as a metric to quantify the value of each training datum to the predictor performance. Data Shapley value uniquely satisfies several natural properties of equitable data valuation. We develop Monte Carlo and gradient-based methods to efficiently estimate data Shapley values in practical settings where complex learning algorithms, including neural networks, are trained on large datasets. In addition to being equitable, extensive experiments across biomedical, image and synthetic data demonstrate that data Shapley has several other benefits: 1) it is more powerful than the popular leave-one-out or leverage score in providing insight on what data is more valuable for a given learning task; 2) low Shapley value data effectively capture outliers and corruptions; 3) high Shapley value data inform what type of new data to acquire to improve the predictor.},
	urldate = {2022-10-16},
	journal = {Proceedings of the 36th International Conference on Machine Learning},
	author = {Ghorbani, Amirata and Zou, James},
	month = jun,
	year = {2019},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@inproceedings{el_balghiti_generalization_2019,
	title = {Generalization {Bounds} in the {Predict}-then-{Optimize} {Framework}},
	volume = {32},
	abstract = {The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced in [Elmachtoub and Grigas, 2017], which called it the Smart Predict-then-Optimize (SPO) loss. Since the SPO loss is nonconvex and noncontinuous, standard results for deriving generalization bounds do not apply. In this work, we provide an assortment of generalization bounds for the SPO loss function. In particular, we derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex set, have poor dependence on the dimension. By exploiting the structure of the SPO loss function and an additional strong convexity assumption on the feasible region, we can dramatically improve the dependence on the dimension via an analysis and corresponding bounds that are akin to the margin guarantees in classification problems.},
	urldate = {2024-04-23},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	publisher = {Curran Associates, Inc.},
	author = {El Balghiti, Othman and Elmachtoub, Adam N. and Grigas, Paul and Tewari, Ambuj},
	year = {2019},
	keywords = {notion},
}

@misc{noauthor_nasdaq_nodate,
	title = {Nasdaq {Data} {Link}},
	url = {https://data.nasdaq.com},
	abstract = {The source for financial, economic, and alternative datasets, serving investment professionals.},
	language = {en},
	urldate = {2024-05-23},
	keywords = {notion},
}

@inproceedings{damodaran_deepjdot_2018,
	address = {Cham},
	title = {{DeepJDOT}: {Deep} {Joint} {Distribution} {Optimal} {Transport} for {Unsupervised} {Domain} {Adaptation}},
	isbn = {978-3-030-01225-0},
	shorttitle = {{DeepJDOT}},
	doi = {10.1007/978-3-030-01225-0_28},
	abstract = {In computer vision, one is often confronted with problems of domain shifts, which occur when one applies a classifier trained on a source dataset to target data sharing similar characteristics (e.g. same classes), but also different latent data structures (e.g. different acquisition conditions). In such a situation, the model will perform poorly on the new data, since the classifier is specialized to recognize visual cues specific to the source domain. In this work we explore a solution, named DeepJDOT, to tackle this problem: through a measure of discrepancy on joint deep representations/labels based on optimal transport, we not only learn new data representations aligned between the source and target domain, but also simultaneously preserve the discriminative information used by the classifier. We applied DeepJDOT to a series of visual recognition tasks, where it compares favorably against state-of-the-art deep domain adaptation methods.},
	language = {en},
	booktitle = {Computer {Vision} – {ECCV} 2018},
	publisher = {Springer International Publishing},
	author = {Damodaran, Bharath Bhushan and Kellenberger, Benjamin and Flamary, Rémi and Tuia, Devis and Courty, Nicolas},
	editor = {Ferrari, Vittorio and Hebert, Martial and Sminchisescu, Cristian and Weiss, Yair},
	year = {2018},
	keywords = {Deep domain adaptation, Optimal transport, notion},
	pages = {467--483},
}

@inproceedings{agrawal_differentiable_2019,
	title = {Differentiable convex optimization layers},
	abstract = {Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.},
	urldate = {2024-04-24},
	booktitle = {Proceedings of the 33rd {International} {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Agrawal, Akshay and Amos, Brandon and Barratt, Shane and Boyd, Stephen and Diamond, Steven and Kolter, J. Zico},
	year = {2019},
	keywords = {notion},
}

@misc{mandi_decision-focused_2023,
	title = {Decision-{Focused} {Learning}: {Foundations}, {State} of the {Art}, {Benchmark} and {Future} {Opportunities}},
	shorttitle = {Decision-{Focused} {Learning}},
	abstract = {Decision-focused learning (DFL) is an emerging paradigm in machine learning which trains a model to optimize decisions, integrating prediction and optimization in an end-to-end system. This paradigm holds the promise to revolutionize decision-making in many real-world applications which operate under uncertainty, where the estimation of unknown parameters within these decision models often becomes a substantial roadblock. This paper presents a comprehensive review of DFL. It provides an in-depth analysis of the various techniques devised to integrate machine learning and optimization models, introduces a taxonomy of DFL methods distinguished by their unique characteristics, and conducts an extensive empirical evaluation of these methods proposing suitable benchmark dataset and tasks for DFL. Finally, the study provides valuable insights into current and potential future avenues in DFL research.},
	publisher = {arXiv},
	author = {Mandi, Jayanta and Kotary, James and Berden, Senne and Mulamba, Maxime and Bucarey, Victor and Guns, Tias and Fioretto, Ferdinando},
	year = {2023},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Mathematics - Optimization and Control, notion},
}

@article{ferber_mipaal_2020,
	title = {{MIPaaL}: {Mixed} {Integer} {Program} as a {Layer}},
	volume = {34},
	abstract = {Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures average accuracy between predicted values and ground truth values. Decision-focused learning explicitly integrates the downstream decision problem when training the predictive model, in order to optimize the quality of decisions induced by the predictions. It has been successfully applied to several limited combinatorial problem classes, such as those that can be expressed as linear programs (LP), and submodular optimization. However, these previous applications have uniformly focused on problems with simple constraints. Here, we enable decision-focused learning for the broad class of problems that can be encoded as a mixed integer linear program (MIP), hence supporting arbitrary linear constraints over discrete and continuous variables. We show how to differentiate through a MIP by employing a cutting planes solution approach, an algorithm that iteratively tightens the continuous relaxation by adding constraints removing fractional solutions. We evaluate our new end-to-end approach on several real world domains and show that it outperforms the standard two phase approaches that treat prediction and optimization separately, as well as a baseline approach of simply applying decision-focused learning to the LP relaxation of the MIP. Lastly, we demonstrate generalization performance in several transfer learning tasks.},
	number = {02},
	journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
	author = {Ferber, Aaron and Wilder, Bryan and Dilkina, Bistra and Tambe, Milind},
	year = {2020},
	keywords = {notion},
	pages = {1504--1511},
}

@misc{wang_data_2023,
	title = {Data {Banzhaf}: {A} {Robust} {Data} {Valuation} {Framework} for {Machine} {Learning}},
	shorttitle = {Data {Banzhaf}},
	url = {http://arxiv.org/abs/2205.15466},
	abstract = {Data valuation has wide use cases in machine learning, including improving data quality and creating economic incentives for data sharing. This paper studies the robustness of data valuation to noisy model performance scores. Particularly, we find that the inherent randomness of the widely used stochastic gradient descent can cause existing data value notions (e.g., the Shapley value and the Leave-one-out error) to produce inconsistent data value rankings across different runs. To address this challenge, we introduce the concept of safety margin, which measures the robustness of a data value notion. We show that the Banzhaf value, a famous value notion that originated from cooperative game theory literature, achieves the largest safety margin among all semivalues (a class of value notions that satisfy crucial properties entailed by ML applications and include the famous Shapley value and Leave-one-out error). We propose an algorithm to efficiently estimate the Banzhaf value based on the Maximum Sample Reuse (MSR) principle. Our evaluation demonstrates that the Banzhaf value outperforms the existing semivalue-based data value notions on several ML tasks such as learning with weighted samples and noisy label detection. Overall, our study suggests that when the underlying ML algorithm is stochastic, the Banzhaf value is a promising alternative to the other semivalue-based data value schemes given its computational advantage and ability to robustly differentiate data quality.},
	urldate = {2024-01-23},
	publisher = {arXiv},
	author = {Wang, Jiachen T. and Jia, Ruoxi},
	month = dec,
	year = {2023},
	note = {arXiv:2205.15466 [cs, stat]},
	keywords = {Computer Science - Computer Science and Game Theory, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@article{noauthor_active_nodate,
	title = {Active {Learning} {Query} {Strategies} for {Classification}, {Regression}, and {Clustering}: {A} {Survey}},
}

@inproceedings{verma_restless_2023,
	title = {Restless {Multi}-{Armed} {Bandits} for {Maternal} and {Child} {Health}: {Results} from {Decision}-{Focused} {Learning}},
	booktitle = {{AAMAS} '23: {Proceedings} of the 2023 {International} {Conference} on {Autonomous} {Agents} and {Multiagent} {Systems}},
	author = {Verma, Shresth and Mate, Aditya and Wang, Kai and Madhiwalla, Neha and Hedge, Aparna and Taneja, Aparna and Tambe, Milind},
	year = {2023},
}

@article{kwon_beta_2022,
	title = {Beta {Shapley}: a {Unified} and {Noise}-reduced {Data} {Valuation} {Framework} for {Machine} {Learning}},
	shorttitle = {Beta {Shapley}},
	url = {http://arxiv.org/abs/2110.14049},
	abstract = {Data Shapley has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. It can effectively identify helpful or harmful data points for a learning algorithm. In this paper, we propose Beta Shapley, which is a substantial generalization of Data Shapley. Beta Shapley arises naturally by relaxing the efficiency axiom of the Shapley value, which is not critical for machine learning settings. Beta Shapley unifies several popular data valuation methods and includes data Shapley as a special case. Moreover, we prove that Beta Shapley has several desirable statistical properties and propose efficient algorithms to estimate it. We demonstrate that Beta Shapley outperforms state-of-the-art data valuation methods on several downstream ML tasks such as: 1) detecting mislabeled training data; 2) learning with subsamples; and 3) identifying points whose addition or removal have the largest positive or negative impact on the model.},
	urldate = {2022-10-16},
	journal = {Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS)},
	author = {Kwon, Yongchan and Zou, James},
	month = jan,
	year = {2022},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}
