@article{singh2023robust,
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  year={2023}
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title = {Epistemic Conservativity and Imprecise Credence},
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@inproceedings{konek2019,
title = {IP Scoring Rules: Foundations and Applications},
author = {Konek, Jason},
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pages = {256--264},
year = {2019},
publisher = {PMLR},
url = {https://proceedings.mlr.press/v103/konek19a.html}
}

@inproceedings{konek2023,
title = {Evaluating Imprecise Forecasts},
author = {Konek, Jason},
booktitle = {Proceedings of the International Symposium on Imprecise Probability: Theories and Applications},
volume = {215},
pages = {270--279},
year = {2023},
publisher = {PMLR},
url = {https://proceedings.mlr.press/v215/konek23a.html}
}
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  title        = {Introduction to Imprecise Probabilities},
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  year         = {2014},
  publisher    = {John Wiley \& Sons},
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}

@incollection{troffaes2014lower,
  title        = {Lower Previsions},
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  booktitle    = {Introduction to Imprecise Probabilities},
  pages        = {159--181},
  year         = {2014},
  publisher    = {John Wiley \& Sons},
  address      = {Chichester}
}
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  author={Sim, Rachael Hwee Ling and Zhang, Yehong and Low, Bryan Kian Hsiang and Jaillet, Patrick},
  booktitle={International Conference on Machine Learning (ICML)},
  volume = 	 {139},
  pages={9691--9701},
  year={2021},
  organization={PMLR},
  url = 	 {https://proceedings.mlr.press/v139/sim21b.html},
}
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  title={Relative utilitarianism},
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@inproceedings{yanagisawa2023proper,
  title={Proper scoring rules for survival analysis},
  author={Yanagisawa, Hiroki},
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  pages={39165--39182},
  year={2023},
  organization={PMLR}
}
@inproceedings{rindt2022survival,
  title={Survival regression with proper scoring rules and monotonic neural networks},
  author={Rindt, David and Hu, Robert and Steinsaltz, David and Sejdinovic, Dino},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1190--1205},
  year={2022},
  organization={PMLR}
}
@article{wu2024elicitationgpt,
  title={ElicitationGPT: Text Elicitation Mechanisms via Language Models},
  author={Wu, Yifan and Hartline, Jason},
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  year={2024}
}
@article{shao2024language,
  title={Language Generation with Strictly Proper Scoring Rules},
  author={Shao, Chenze and Meng, Fandong and Liu, Yijin and Zhou, Jie},
  journal={arXiv preprint arXiv:2405.18906},
  year={2024}
}
@article{pinson2013wind,
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@article{pinson2012evaluating,
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  year={2024}
}
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@article{gopalan2021omnipredictors,
  title={Omnipredictors},
  author={Gopalan, Parikshit and Kalai, Adam Tauman and Reingold, Omer and Sharan, Vatsal and Wieder, Udi},
  journal={arXiv preprint arXiv:2109.05389},
  year={2021}
}
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  title={The foundations of statistics},
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@article{murphy1988decomposition,
  title        = {A new vector partition of the probability score},
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@article{dawid2007,
  title        = {The geometry of proper scoring rules},
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  volume       = {35},
  number       = {5},
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}

@article{buja2005loss,
  title        = {Loss Functions for Binary Classifiers: a survey of techniques, algorithms, and applications},
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}

@article{hansen2020proper,
  title        = {Proper Scoring Rules and Their Applications in Machine Learning},
  author       = {Hansen, Peter R. and others},
  journal      = {Journal of Machine Learning Research},
  volume       = {21},
  pages        = {1--28},
  year         = {2020}
}
@article{gneiting2007strictly,
  title={Strictly proper scoring rules, prediction, and estimation},
  author={Gneiting, Tilmann and Raftery, Adrian E},
  journal={Journal of the American statistical Association},
  volume={102},
  number={477},
  pages={359--378},
  year={2007},
  publisher={Taylor \& Francis}
}
@article{volpi2018generalizing,
  title={Generalizing to unseen domains via adversarial data augmentation},
  author={Volpi, Riccardo and Namkoong, Hongseok and Sener, Ozan and Duchi, John C and Murino, Vittorio and Savarese, Silvio},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}
@article{singh2024domain,
  title={Domain Generalisation via Imprecise Learning},
  author={Singh, Anurag and Chau, Siu Lun and Bouabid, Shahine and Muandet, Krikamol},
  journal={arXiv preprint arXiv:2404.04669},
  year={2024}
}
@article{brown2020language,
  title={Language models are few-shot learners},
  author={Brown, Tom B},
  journal={arXiv preprint arXiv:2005.14165},
  year={2020}
}
@inproceedings{recht2019imagenet,
  title={Do imagenet classifiers generalize to imagenet?},
  author={Recht, Benjamin and Roelofs, Rebecca and Schmidt, Ludwig and Shankar, Vaishaal},
  booktitle={International conference on machine learning},
  pages={5389--5400},
  year={2019},
  organization={PMLR}
}
@phdthesis{arjovski2021,
  title = {Out of {{Distribution Generalization}} in {{Machine Learning}}},
  author = {Arjovski, Martin},
  year = {2021},
  school = {New York University},
  file = {/Users/sfoell/Zotero/storage/H4UIJK35/Arjovski - 2021 - Out of Distribution Generalization in Machine Lear.pdf}
}

@book{augustin2014,
  title = {Introduction to Imprecise Probabilities},
  editor = {Augustin, Thomas},
  year = {2014},
  series = {Wiley Series in Probability and Statistics},
  publisher = {{John Wiley \& Sons Inc}},
  address = {{Chichester, West Sussex}},
  isbn = {978-1-118-76314-8 978-1-118-76313-1},
  lccn = {QA273},
  keywords = {MATHEMATICS / Probability \& Statistics / General,Probabilities}
}

@inproceedings{brault2019,
  title = {Infinite {{Task Learning}} in {{RKHSs}}},
  booktitle = {Proc. {{Twenty-Second Int}}. {{Conf}}. {{Artif}}. {{Intell}}. {{Stat}}.},
  author = {Brault, Romain and Lambert, Alex and Szabo, Zoltan and Sangnier, Maxime and {d'Alche-Buc}, Florence},
  editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
  year = {2019},
  month = apr,
  series = {Proceedings of {{Machine Learning Research}}},
  volume = {89},
  pages = {1294--1302},
  publisher = {{PMLR}},
  abstract = {Machine learning has witnessed tremendous success in solving tasks depending on a single hyperparameter. When considering simultaneously a finite number of tasks, multi-task learning enables one to account for the similarities of the tasks via appropriate regularizers. A step further consists of learning a continuum of tasks for various loss functions. A promising approach, called Parametric Task Learning, has paved the way in the continuum setting for affine models and piecewise-linear loss functions. In this work, we introduce a novel approach called Infinite Task Learning whose goal is to learn a function whose output is a function over the hyperparameter space. We leverage tools from operator-valued kernels and the associated vector-valued RKHSs that provide an explicit control over the role of the hyperparameters, and also allows us to consider new type of constraints. We provide generalization guarantees to the suggested scheme and illustrate its efficiency in cost-sensitive classification, quantile regression and density level set estimation.},
  file = {/Users/sfoell/Zotero/storage/6BXBHIJ6/Brault et al. - 2019 - Infinite Task Learning in RKHSs.pdf;/Users/sfoell/Zotero/storage/G6WAF3JQ/brault19a-supp.pdf}
}

@inproceedings{eastwood2022,
  title = {Probable {{Domain Generalization}} via {{Quantile Risk Minimization}}},
  booktitle = {Adv. {{Neural Inf}}. {{Process}}. {{Syst}}.},
  author = {Eastwood, Cian and Robey, Alexander and Singh, Shashank and {von K{\"u}gelgen}, Julius and Hassani, Hamed and Pappas, George J. and Sch{\"o}lkopf, Bernhard},
  year = {2022},
  month = oct,
  volume = {35},
  eprint = {2207.09944},
  primaryclass = {cs, stat},
  publisher = {{Curran Associates, Inc.}},
  urldate = {2022-10-17},
  abstract = {Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the {$\alpha$}-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability {$\alpha$}. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm, and prove: (i) a generalization bound for EQRM; and (ii) that EQRM recovers the causal predictor as {$\alpha$} \textrightarrow{} 1. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG, and demonstrate that EQRM outperforms state-of-theart baselines on CMNIST and several datasets from WILDS and DomainBed.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Computer Vision and Pattern Recognition,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {/Users/sfoell/Zotero/storage/34RCF6YG/Eastwood et al. - 2022 - Probable Domain Generalization via Quantile Risk M.pdf}
}

@misc{frohlich2022,
  title = {Risk {{Measures}} and {{Upper Probabilities}}: {{Coherence}} and {{Stratification}}},
  shorttitle = {Risk {{Measures}} and {{Upper Probabilities}}},
  author = {Fr{\"o}hlich, Christian and Williamson, Robert C.},
  year = {2022},
  month = jun,
  number = {arXiv:2206.03183},
  eprint = {2206.03183},
  primaryclass = {cs, math, stat},
  publisher = {{arXiv}},
  urldate = {2023-03-07},
  abstract = {Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a mathematical foundation for machine learning. We systematically examine a powerful and rich class of such alternatives, known variously as spectral risk measures, Choquet integrals or Lorentz norms. We present a range of characterization results, and demonstrate what makes this spectral family so special. In doing so we demonstrate a natural stratification of all coherent risk measures in terms of the upper probabilities that they induce by exploiting results from the theory of rearrangement invariant Banach spaces. We empirically demonstrate how this new approach to uncertainty helps tackling practical machine learning problems.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Mathematics - Statistics Theory},
  file = {/Users/sfoell/Zotero/storage/ZMQLWACR/Fröhlich and Williamson - 2022 - Risk Measures and Upper Probabilities Coherence a.pdf}
}

@book{gorban2017,
  title = {The {{Statistical Stability Phenomenon}}},
  author = {Gorban, Igor I.},
  year = {2017},
  series = {Mathematical {{Engineering}}},
  edition = {1st ed. 2017},
  publisher = {{Springer International Publishing : Imprint: Springer}},
  address = {{Cham}},
  doi = {10.1007/978-3-319-43585-5},
  abstract = {This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations - the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability. The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals},
  isbn = {978-3-319-43585-5},
  lccn = {519},
  keywords = {Applied mathematics,Complex Systems,Dynamical systems,Engineering mathematics,Mathematical and Computational Engineering,Mathematical Applications in the Physical Sciences,Mathematical physics,Measurement,Measurement Science and Instrumentation,Physical measurements,Statistical physics,Statistical Physics and Dynamical Systems,Statistics,Statistics for Engineering; Physics; Computer Science; Chemistry and Earth Sciences},
  file = {/Users/sfoell/Zotero/storage/GDGQKZQD/Gorban - 2017 - The Statistical Stability Phenomenon.pdf}
}

@article{hullermeier2021,
  title = {Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods},
  author = {H{\"u}llermeier, Eyke and Waegeman, Willem},
  year = {2021},
  month = mar,
  journal = {Machine Learning},
  volume = {110},
  number = {3},
  pages = {457--506},
  issn = {1573-0565},
  doi = {10.1007/s10994-021-05946-3},
  abstract = {The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.},
  file = {/Users/sfoell/Zotero/storage/TM4VS7AQ/Hüllermeier and Waegeman - 2021 - Aleatoric and epistemic uncertainty in machine lea.pdf}
}

@inproceedings{li2021,
  title = {Tilted {{Empirical Risk Minimization}}},
  booktitle = {Int. {{Conf}}. {{Learn}}. {{Represent}}.},
  author = {Li, Tian and Beirami, Ahmad and Sanjabi, Maziar and Smith, Virginia},
  year = {2021},
  month = mar,
  eprint = {2007.01162},
  primaryclass = {cs, math, stat},
  publisher = {{arXiv}},
  urldate = {2022-10-17},
  abstract = {Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address these problems individually, in this work, we explore them through a unified framework\textemdash tilted empirical risk minimization (TERM). In particular, we show that it is possible to flexibly tune the impact of individual losses through a straightforward extension to ERM using a hyperparameter called the tilt. We provide several interpretations of the resulting framework: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variancereduction properties that can benefit generalization; and can be viewed as a smooth approximation to a superquantile method. We develop batch and stochastic firstorder optimization methods for solving TERM, and show that the problem can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. TERM is not only competitive with existing solutions tailored to these individual problems, but can also enable entirely new applications, such as simultaneously addressing outliers and promoting fairness.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Information Theory,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {/Users/sfoell/Zotero/storage/BKYHLBPU/Li et al. - 2021 - Tilted Empirical Risk Minimization.pdf}
}

@misc{moayeri2022,
  title = {Explicit {{Tradeoffs}} between {{Adversarial}} and {{Natural Distributional Robustness}}},
  author = {Moayeri, Mazda and Banihashem, Kiarash and Feizi, Soheil},
  year = {2022},
  month = sep,
  number = {arXiv:2209.07592},
  eprint = {2209.07592},
  primaryclass = {cs},
  publisher = {{arXiv}},
  urldate = {2023-03-03},
  abstract = {Several existing works study either adversarial or natural distributional robustness of deep neural networks separately. In practice, however, models need to enjoy both types of robustness to ensure reliability. In this work, we bridge this gap and show that in fact, explicit tradeoffs exist between adversarial and natural distributional robustness. We first consider a simple linear regression setting on Gaussian data with disjoint sets of core and spurious features. In this setting, through theoretical and empirical analysis, we show that (i) adversarial training with 1 and 2 norms increases the model reliance on spurious features; (ii) For {$\infty$} adversarial training, spurious reliance only occurs when the scale of the spurious features is larger than that of the core features; (iii) adversarial training can have an unintended consequence in reducing distributional robustness, specifically when spurious correlations are changed in the new test domain. Next, we present extensive empirical evidence, using a test suite of twenty adversarially trained models evaluated on five benchmark datasets (ObjectNet, RIVAL10, Salient ImageNet-1M, ImageNet-9, Waterbirds), that adversarially trained classifiers rely on backgrounds more than their standardly trained counterparts, validating our theoretical results. We also show that spurious correlations in training data (when preserved in the test domain) can improve adversarial robustness, revealing that previous claims that adversarial vulnerability is rooted in spurious correlations are incomplete.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Computer Vision and Pattern Recognition,Computer Science - Machine Learning},
  file = {/Users/sfoell/Zotero/storage/YJDD6V99/Moayeri et al. - 2022 - Explicit Tradeoffs between Adversarial and Natural.pdf}
}

@inproceedings{pmlr-v162-robey22a,
  title = {Probabilistically Robust Learning: {{Balancing}} Average and Worst-Case Performance},
  booktitle = {Proc. 39th {{Int}}. {{Conf}}. {{Mach}}. {{Learn}}.},
  author = {Robey, Alexander and Chamon, Luiz and Pappas, George J. and Hassani, Hamed},
  editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
  year = {2022},
  month = jul,
  series = {Proceedings of Machine Learning Research},
  volume = {162},
  pages = {18667--18686},
  publisher = {{PMLR}},
  abstract = {Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness. Our code is available at: https://github.com/arobey1/advbench.},
  pdf = {https://proceedings.mlr.press/v162/robey22a/robey22a.pdf},
  file = {/Users/sfoell/Zotero/storage/IXX3MEKM/Robey et al. - 2022 - Probabilistically robust learning Balancing avera.pdf}
}

@inproceedings{pmlr-v97-williamson19a,
  title = {Fairness Risk Measures},
  booktitle = {Proc. 36th {{Int}}. {{Conf}}. {{Mach}}. {{Learn}}.},
  author = {Williamson, Robert and Menon, Aditya},
  editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  year = {2019},
  month = jun,
  series = {Proceedings of Machine Learning Research},
  volume = {97},
  pages = {6786--6797},
  publisher = {{PMLR}},
  abstract = {Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either binary sensitive features (thus precluding categorical or real-valued sensitive groups), or result in non-convex objectives (thus adversely affecting the optimisation landscape). In this paper, we propose a new definition of fairness that generalises some existing proposals, while allowing for generic sensitive features and resulting in a convex objective. The key idea is to enforce that the expected losses (or risks) across each subgroup induced by the sensitive feature are commensurate. We show how this relates to the rich literature on risk measures from mathematical finance. As a special case, this leads to a new convex fairness-aware objective based on minimising the conditional value at risk (CVaR).},
  file = {/Users/sfoell/Zotero/storage/7VWIMIAK/Williamson and Menon - 2019 - Fairness risk measures.pdf;/Users/sfoell/Zotero/storage/J43XSDJP/williamson19a-supp.pdf}
}

@article{rahimian2022,
  title = {Distributionally {{Robust Optimization}}: {{A Review}}},
  shorttitle = {Distributionally {{Robust Optimization}}},
  author = {Rahimian, Hamed and Mehrotra, Sanjay},
  year = {2022},
  month = jul,
  journal = {Open J. Math. Optim.},
  volume = {3},
  eprint = {1908.05659},
  primaryclass = {cs, math, stat},
  pages = {1--85},
  issn = {2777-5860},
  doi = {10.5802/ojmo.15},
  urldate = {2023-04-21},
  abstract = {The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Mathematics - Optimization and Control,Statistics - Machine Learning},
  file = {/Users/sfoell/Zotero/storage/TLS3YLND/Rahimian and Mehrotra - 2022 - Distributionally Robust Optimization A Review.pdf}
}

@inproceedings{takeuchi2013,
  title = {Parametric {{Task Learning}}},
  booktitle = {Adv. {{Neural Inf}}. {{Process}}. {{Syst}}.},
  author = {Takeuchi, Ichiro and Hongo, Tatsuya and Sugiyama, Masashi and Nakajima, Shinichi},
  editor = {Burges, C. J. and Bottou, L. and Welling, M. and Ghahramani, Z. and Weinberger, K. Q.},
  year = {2013},
  volume = {26},
  publisher = {{Curran Associates, Inc.}},
  keywords = {⛔ No DOI found},
  file = {/Users/sfoell/Zotero/storage/87JQ8QUR/supp.pdf;/Users/sfoell/Zotero/storage/8EGCDG7B/Takeuchi et al. - 2013 - Parametric Task Learning.pdf}
}

@article{wald1945,
  title = {Statistical {{Decision Functions Which Minimize}} the {{Maximum Risk}}},
  author = {Wald, Abraham},
  year = {1945},
  journal = {Ann. Math.},
  volume = {46},
  number = {2},
  eprint = {1969022},
  eprinttype = {jstor},
  pages = {265--280},
  publisher = {{Annals of Mathematics}},
  issn = {0003486X},
  doi = {10.2307/1969022},
  urldate = {2023-03-09},
  file = {/Users/sfoell/Zotero/storage/RWZSR2G3/Wald - 1945 - Statistical Decision Functions Which Minimize the .pdf}
}

@misc{zhang2021,
  title = {Adaptive {{Risk Minimization}}: {{Learning}} to {{Adapt}} to {{Domain Shift}}},
  shorttitle = {Adaptive {{Risk Minimization}}},
  author = {Zhang, Marvin and Marklund, Henrik and Dhawan, Nikita and Gupta, Abhishek and Levine, Sergey and Finn, Chelsea},
  year = {2021},
  month = dec,
  number = {arXiv:2007.02931},
  eprint = {2007.02931},
  primaryclass = {cs, stat},
  publisher = {{arXiv}},
  urldate = {2023-02-17},
  abstract = {A fundamental assumption of most machine learning algorithms is that the training and test data are drawn from the same underlying distribution. However, this assumption is violated in almost all practical applications: machine learning systems are regularly tested under distribution shift, due to changing temporal correlations, atypical end users, or other factors. In this work, we consider the problem setting of domain generalization, where the training data are structured into domains and there may be multiple test time shifts, corresponding to new domains or domain distributions. Most prior methods aim to learn a single robust model or invariant feature space that performs well on all domains. In contrast, we aim to learn models that adapt at test time to domain shift using unlabeled test points. Our primary contribution is to introduce the framework of adaptive risk minimization (ARM), in which models are directly optimized for effective adaptation to shift by learning to adapt on the training domains. Compared to prior methods for robustness, invariance, and adaptation, ARM methods provide performance gains of 1-4\% test accuracy on a number of image classification problems exhibiting domain shift.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {/Users/sfoell/Zotero/storage/T2YWQQLH/Zhang et al. - 2021 - Adaptive Risk Minimization Learning to Adapt to D.pdf}
}
