%% Ours

@article{singh2021hybrid,
  title={A Hybrid 2-stage Neural Optimization for Pareto Front Extraction},
  author={Singh, Gurpreet and Gupta, Soumyajit and Lease, Matthew and Dawson, Clint},
  journal={arXiv preprint arXiv:2101.11684},
  year={2021}
}

@book{cohon2004multiobjective,
  title={Multiobjective programming and planning},
  author={Cohon, Jared L},
  volume={140},
  year={2004}
}

@article{swezey2021pirank,
  title={PiRank: Scalable Learning To Rank via Differentiable Sorting},
  author={Swezey, Robin and Grover, Aditya and Charron, Bruno and Ermon, Stefano},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  year={2021}
}

@article{raissi2019physics,
  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
  journal={Journal of Computational Physics},
  volume={378},
  pages={686--707},
  year={2019},
  publisher={Elsevier}
}

@article{csaji2001approximation,
  title={Approximation with artificial neural networks},
  author={Cs{\'a}ji, Bal{\'a}zs Csan{\'a}d and others},
  journal={Faculty of Sciences, Etvs Lornd University, Hungary},
  volume={24},
  number={48},
  pages={7},
  year={2001},
  publisher={Citeseer}
}

@article{lu2017expressive,
  title={The expressive power of neural networks: A view from the width},
  author={Lu, Zhou and Pu, Hongming and Wang, Feicheng and Hu, Zhiqiang and Wang, Liwei},
  journal={arXiv preprint arXiv:1709.02540},
  year={2017}
}

@inproceedings{safran2017depth,
  title={Depth-width tradeoffs in approximating natural functions with neural networks},
  author={Safran, Itay and Shamir, Ohad},
  booktitle={International Conference on Machine Learning},
  pages={2979--2987},
  year={2017},
  organization={PMLR}
}

@article{gupta2021tobepareto,
  title={To Be or Not To Be Pareto Optimal for Multi Task Learning},
  author={Gupta, Soumyajit and Singh, Gurpreet and Lease, Matthew and Dawson, Clint},
  journal={arXiv preprint arXiv:},
  year={2021}
}

@inproceedings{sabour2017dynamic,
  title={Dynamic routing between capsules},
  author={Sabour, Sara and Frosst, Nicholas and Hinton, Geoffrey E},
  booktitle={Proceedings of the 31st International Conference on Neural Information Processing Systems},
  pages={3859--3869},
  year={2017}
}

@misc{chollet2015,
author = {François Chollet },
title = {keras},
year = {2015},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/fchollet/keras}},
commit = {5bcac37}
}


@inproceedings{kingma2014adam,
  author    = {Diederik P. Kingma and
               Jimmy Ba},
  editor    = {Yoshua Bengio and
               Yann LeCun},
  title     = {Adam: {A} Method for Stochastic Optimization},
  booktitle = {3rd International Conference on Learning Representations, {ICLR} 2015,
               San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings},
  year      = {2015},
  url       = {http://arxiv.org/abs/1412.6980},
  timestamp = {Thu, 25 Jul 2019 14:25:37 +0200},
  biburl    = {https://dblp.org/rec/journals/corr/KingmaB14.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}



@inproceedings{levi2006application,
  title={An application of analytical multi-objective optimization to truss structures},
  author={Levi, Francesco and Gobbi, Massimiliano},
  booktitle={11th AIAA/ISSMO multidisciplinary analysis and optimization conference},
  pages={6975},
  year={2006}
}

@article{gobbi2015analytical,
  title={On the analytical derivation of the Pareto-optimal set with applications to structural design},
  author={Gobbi, Massimiliano and Levi, F and Mastinu, Gianpiero and Previati, Giorgio},
  journal={Structural and Multidisciplinary Optimization},
  volume={51},
  number={3},
  pages={645--657},
  year={2015},
  publisher={Springer}
}

@article{marucsciac1982fritz,
  title={On Fritz John type optimality criterion in multi-objective optimization},
  author={Maru{\c{s}}ciac, I},
  journal={Mathematica-Rev. Anal. Num{\'e}r. Th{\'e}or. Approx.},
  pages={109--114},
  year={1982}
}

%% Engineering

@article{marler2004survey,
	title={Survey of multi-objective optimization methods for engineering},
	author={Marler, R Timothy and Arora, Jasbir S},
	journal={Structural and multidisciplinary optimization},
	volume={26},
	number={6},
	pages={369--395},
	year={2004},
	publisher={Springer}
}



@article{deb2013evolutionary,
	title={An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints},
	author={Deb, Kalyanmoy and Jain, Himanshu},
	journal={IEEE transactions on evolutionary computation},
	volume={18},
	number={4},
	pages={577--601},
	year={2013},
	publisher={IEEE}
}

@book{boyd2004convex,
	title={Convex optimization},
	author={Boyd, Stephen and Boyd, Stephen P and Vandenberghe, Lieven},
	year={2004},
	publisher={Cambridge university press}
}

@book{miettinen2012nonlinear,
	title={Nonlinear multiobjective optimization},
	author={Miettinen, Kaisa},
	volume={12},
	year={2012},
	publisher={Springer Science \& Business Media}
}

@article{ghane2015new,
	title={A new scalarization method for finding the efficient frontier in non-convex multi-objective problems},
	author={Ghane-Kanafi, A and Khorram, E},
	journal={Applied Mathematical Modelling},
	volume={39},
	number={23-24},
	pages={7483--7498},
	year={2015},
	publisher={Elsevier}
}

@article{pirouz2016computational,
	title={A computational approach based on the $\varepsilon$-constraint method in multi-objective optimization problems},
	author={Pirouz, Behzad and Khorram, Esmaile},
	journal={Advances and Applications in Statistics},
	volume={49},
	number={6},
	pages={453},
	year={2016},
	publisher={Pushpa Publishing House}
}

@article{das1998normal,
	title={Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems},
	author={Das, Indraneel and Dennis, John E},
	journal={SIAM journal on optimization},
	volume={8},
	number={3},
	pages={631--657},
	year={1998},
	publisher={SIAM}
}

@article{pareto1906manuale,
	title={Manuale di economica politica, societa editrice libraria. milan},
	author={Pareto, Vilfredo},
	journal={English translation as Manual of Political Economy, Kelley, New York},
	year={1906}
}

@article{van1994saddle,
	title={A saddle-point characterization of Pareto optima},
	author={Van Rooyen, M and Zhou, X and Zlobec, Sanjo},
	journal={Mathematical programming},
	volume={67},
	number={1},
	pages={77--88},
	year={1994},
	publisher={Springer}
}

@article{ehrgott2005saddle,
	title={Saddle points and Pareto points in multiple objective programming},
	author={Ehrgott, Matthias and Wiecek, Margaret M},
	journal={Journal of Global Optimization},
	volume={32},
	number={1},
	pages={11--33},
	year={2005},
	publisher={Springer}
}

@article{benzi2005numerical,
  title={Numerical solution of saddle point problems},
  author={Benzi, Michele and Golub, Gene H and Liesen, J{\"o}rg},
  journal={Acta numerica},
  volume={14},
  pages={1--137},
  year={2005},
  publisher={Cambridge University Press}
}

@incollection{benzi2008some,
  title={Some preconditioning techniques for saddle point problems},
  author={Benzi, Michele and Wathen, Andrew J},
  booktitle={Model order reduction: theory, research aspects and applications},
  pages={195--211},
  year={2008},
  publisher={Springer}
}

@article{dreves2011solution,
  title={On the solution of the KKT conditions of generalized Nash equilibrium problems},
  author={Dreves, Axel and Facchinei, Francisco and Kanzow, Christian and Sagratella, Simone},
  journal={SIAM Journal on Optimization},
  volume={21},
  number={3},
  pages={1082--1108},
  year={2011},
  publisher={SIAM}
}

%% MTL

@article{zhang2007moea,
	title={MOEA/D: A multiobjective evolutionary algorithm based on decomposition},
	author={Zhang, Qingfu and Li, Hui},
	journal={IEEE Transactions on evolutionary computation},
	volume={11},
	number={6},
	pages={712--731},
	year={2007},
	publisher={IEEE}
}

@inproceedings{sener2018multi,
  title={Multi-task learning as multi-objective optimization},
  author={Sener, Ozan and Koltun, Vladlen},
  booktitle={Proceedings of the 32nd International Conference on Neural Information Processing Systems},
  pages={525--536},
  year={2018}
}

@inproceedings{ha2016hypernetworks,
  author    = {David Ha and
               Andrew M. Dai and
               Quoc V. Le},
  title     = {HyperNetworks},
  booktitle = {5th International Conference on Learning Representations, {ICLR} 2017,
               Toulon, France, April 24-26, 2017, Conference Track Proceedings},
  publisher = {OpenReview.net},
  year      = {2017},
  url       = {https://openreview.net/forum?id=rkpACe1lx},
  timestamp = {Thu, 25 Jul 2019 14:26:04 +0200},
  biburl    = {https://dblp.org/rec/conf/iclr/HaDL17.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

@article{lin2021controllable,
  title={Controllable pareto multi-task learning},
  author={Lin, Xi and Yang, Zhiyuan and Zhang, Qingfu and Kwong, Sam},
  journal={arXiv preprint arXiv:2010.06313},
  year={2020}
}

@inproceedings{navon2021learning,
  title={Learning the Pareto Front with Hypernetworks},
  author={Navon, Aviv and Shamsian, Aviv and Fetaya, Ethan and Chechik, Gal},
  booktitle={International Conference on Learning Representations},
  year={2021}
}

@article{deist2021multi,
  title={Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization},
  author={Deist, Timo M and Grewal, Monika and Dankers, Frank JWM and Alderliesten, Tanja and Bosman, Peter AN},
  journal={arXiv preprint arXiv:2102.04523},
  year={2021}
}

@article{lin2019pareto,
  title={Pareto multi-task learning},
  author={Lin, Xi and Zhen, Hui-Ling and Li, Zhenhua and Zhang, Qing-Fu and Kwong, Sam},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@inproceedings{mahapatra2020multi,
  title={Multi-task learning with user preferences: Gradient descent with controlled ascent in pareto optimization},
  author={Mahapatra, Debabrata and Rajan, Vaibhav},
  booktitle={International Conference on Machine Learning},
  pages={6597--6607},
  year={2020},
  organization={PMLR}
}

@inproceedings{ma2020efficient,
  title={Efficient continuous pareto exploration in multi-task learning},
  author={Ma, Pingchuan and Du, Tao and Matusik, Wojciech},
  booktitle={International Conference on Machine Learning},
  pages={6522--6531},
  year={2020},
  organization={PMLR}
}

%% Application

@article{caton2020fairness,
	title={Fairness in Machine Learning: A Survey},
	author={Caton, Simon and Haas, Christian},
	journal={arXiv preprint arXiv:2010.04053},
	year={2020}
}

@article{wu2021multi,
	title={Multi-FR: A Multi-Objective Optimization Method for Achieving Two-sided Fairness in E-commerce Recommendation},
	author={Wu, Haolun and Ma, Chen and Mitra, Bhaskar and Diaz, Fernando and Liu, Xue},
	journal={arXiv preprint arXiv:2105.02951},
	year={2021}
}

@inproceedings{geden2021fair,
	title={Fair and Interpretable Algorithmic Hiring using Evolutionary Many Objective Optimization},
	author={Geden, Michael and Andrews, Joshua},
	booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
	volume={35},
	number={17},
	pages={14795--14803},
	year={2021}
}

@article{bai2020multi,
	title={Multi-task gradient descent for multi-task learning},
	author={Bai, Lu and Ong, Yew-Soon and He, Tiantian and Gupta, Abhishek},
	journal={Memetic Computing},
	volume={12},
	number={4},
	pages={355--369},
	year={2020},
	publisher={Springer}
}

@inproceedings{xiao2017fairness,
	title={Fairness-aware group recommendation with pareto-efficiency},
	author={Xiao, Lin and Min, Zhang and Yongfeng, Zhang and Zhaoquan, Gu and Yiqun, Liu and Shaoping, Ma},
	booktitle={Proceedings of the Eleventh ACM Conference on Recommender Systems},
	pages={107--115},
	year={2017}
}

@inproceedings{ribeiro2012pareto,
	title={Pareto-efficient hybridization for multi-objective recommender systems},
	author={Ribeiro, Marco Tulio and Lacerda, Anisio and Veloso, Adriano and Ziviani, Nivio},
	booktitle={Proceedings of the sixth ACM conference on Recommender systems},
	pages={19--26},
	year={2012}
}

@article{wang2020multi,
	title={Multi-objective optimization for location-based and preferences-aware recommendation},
	author={Wang, Shanfeng and Gong, Maoguo and Wu, Yue and Zhang, Mingyang},
	journal={Information Sciences},
	volume={513},
	pages={614--626},
	year={2020},
	publisher={Elsevier}
}

@article{xiao2017fashion,
  title={Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms},
  author={Xiao, Han and Rasul, Kashif and Vollgraf, Roland},
  journal={arXiv preprint arXiv:1708.07747},
  year={2017}
}

@inproceedings{fu2020fairness,
	title={Fairness-aware explainable recommendation over knowledge graphs},
	author={Fu, Zuohui and Xian, Yikun and Gao, Ruoyuan and Zhao, Jieyu and Huang, Qiaoying and Ge, Yingqiang and Xu, Shuyuan and Geng, Shijie and Shah, Chirag and Zhang, Yongfeng and others},
	booktitle={Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval},
	pages={69--78},
	year={2020}
}

@article{azadjalal2017trust,
	title={A trust-aware recommendation method based on Pareto dominance and confidence concepts},
	author={Azadjalal, Mohammad Mahdi and Moradi, Parham and Abdollahpouri, Alireza and Jalili, Mahdi},
	journal={Knowledge-Based Systems},
	volume={116},
	pages={130--143},
	year={2017},
	publisher={Elsevier}
}

@inproceedings{liu2019skyrec,
	title={SkyRec: Finding Pareto Optimal Groups},
	author={Liu, Jinfei and Xiong, Li and Pei, Jian and Luo, Jun and Zhang, Haoyu and Zhang, Si},
	booktitle={Proceedings of the 28th ACM International Conference on Information and Knowledge Management},
	pages={2913--2916},
	year={2019}
}

@inproceedings{sacharidis2019top,
	title={Top-N group recommendations with fairness},
	author={Sacharidis, Dimitris},
	booktitle={Proceedings of the 34th ACM/SIGAPP symposium on applied computing},
	pages={1663--1670},
	year={2019}
}

@article{balashankar2019fair,
  title={What is fair? exploring pareto-efficiency for fairness constrained classifiers},
  author={Balashankar, Ananth and Lees, Alyssa and Welty, Chris and Subramanian, Lakshminarayanan},
  journal={arXiv preprint arXiv:1910.14120},
  year={2019}
}

@inproceedings{martinez2020minimax,
  title={Minimax pareto fairness: A multi objective perspective},
  author={Martinez, Natalia and Bertran, Martin and Sapiro, Guillermo},
  booktitle={International Conference on Machine Learning},
  pages={6755--6764},
  year={2020},
  organization={PMLR}
}

@article{valdivia2021fair,
  title={How fair can we go in machine learning? Assessing the boundaries of accuracy and fairness},
  author={Valdivia, Ana and S{\'a}nchez-Monedero, Javier and Casillas, Jorge},
  journal={International Journal of Intelligent Systems},
  volume={36},
  number={4},
  pages={1619--1643},
  year={2021},
  publisher={Wiley Online Library}
}

@article{wei2020fairness,
  title={The Fairness-Accuracy Pareto Front},
  author={Wei, Susan and Niethammer, Marc},
  journal={arXiv preprint arXiv:2008.10797},
  year={2020}
}

@article{milojkovic2019multi,
	title={Multi-gradient descent for multi-objective recommender systems},
	author={Milojkovic, Nikola and Antognini, Diego and Bergamin, Giancarlo and Faltings, Boi and Musat, Claudiu},
	journal={arXiv preprint arXiv:2001.00846},
	year={2019}
}

@inproceedings{hsieh2015pu,
	title={PU learning for matrix completion},
	author={Hsieh, Cho-Jui and Natarajan, Nagarajan and Dhillon, Inderjit},
	booktitle={International Conference on Machine Learning},
	pages={2445--2453},
	year={2015},
	organization={PMLR}
}

@article{crawshaw2020multi,
	title={Multi-Task Learning with Deep Neural Networks: A Survey},
	author={Crawshaw, Michael},
	journal={arXiv preprint arXiv:2009.09796},
	year={2020}
}

@inproceedings{friedler2019comparative,
  title={A comparative study of fairness-enhancing interventions in machine learning},
  author={Friedler, Sorelle A and Scheidegger, Carlos and Venkatasubramanian, Suresh and Choudhary, Sonam and Hamilton, Evan P and Roth, Derek},
  booktitle={Proceedings of the conference on fairness, accountability, and transparency},
  pages={329--338},
  year={2019}
}

@inproceedings{abou2012note,
  title={A note on metric properties for some divergence measures: The Gaussian case},
  author={Abou-Moustafa, Karim T and Ferrie, Frank P},
  booktitle={Asian Conference on Machine Learning},
  pages={1--15},
  year={2012},
  organization={PMLR}
}

@inproceedings{tanaka1995ga,
  title={GA-based decision support system for multicriteria optimization},
  author={Tanaka, Masahiro and Watanabe, Hikaru and Furukawa, Yasuyuki and Tanino, Tetsuzo},
  booktitle={1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century},
  volume={2},
  pages={1556--1561},
  year={1995},
  organization={IEEE}
}

@article{zhang2008multiobjective,
  title={Multiobjective optimization test instances for the CEC 2009 special session and competition},
  author={Zhang, Qingfu and Zhou, Aimin and Zhao, Shizheng and Suganthan, Ponnuthurai Nagaratnam and Liu, Wudong and Tiwari, Santosh},
  year={2008},
  publisher={Colchester, UK}
}

@inproceedings{raza2020regularized,
  title={A Regularized Model to Trade-off between Accuracy and Diversity in a News Recommender System},
  author={Raza, Shaina and Ding, Chen},
  booktitle={2020 IEEE International Conference on Big Data (Big Data)},
  pages={551--560},
  year={2020},
  organization={IEEE}
}

@inproceedings{gao2020simple,
  title={A Simple, Effective and Extendible Approach to Deep Multi-task Learning},
  author={Gao, Yang and Li, Yi-Fan and Lin, Yu and Tao, Hemeng and Khan, Latifur},
  booktitle={2020 IEEE International Conference on Big Data (Big Data)},
  pages={924--929},
  year={2020},
  organization={IEEE}
}

@article{lecun1998gradient,
  title={Gradient-based learning applied to document recognition},
  author={LeCun, Yann and Bottou, L{\'e}on and Bengio, Yoshua and Haffner, Patrick},
  journal={Proceedings of the IEEE},
  volume={86},
  number={11},
  pages={2278--2324},
  year={1998},
  publisher={Ieee}
}

@article{zitzler1999multiobjective,
  title={Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach},
  author={Zitzler, Eckart and Thiele, Lothar},
  journal={IEEE transactions on Evolutionary Computation},
  volume={3},
  number={4},
  pages={257--271},
  year={1999},
  publisher={IEEE}
}

@article{evtushenko2013nonuniform,
  title={Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy},
  author={Evtushenko, Yu G and Posypkin, Mikhail Anatol'evich},
  journal={Computational Mathematics and Mathematical Physics},
  volume={53},
  number={2},
  pages={144--157},
  year={2013},
  publisher={Springer}
}

@article{jain2017non,
  title={Non-convex optimization for machine learning},
  author={Jain, Prateek and Kar, Purushottam and others},
  journal={Foundations and Trends{\textregistered} in Machine Learning},
  volume={10},
  number={3-4},
  pages={142--363},
  year={2017},
  publisher={Now Publishers, Inc.}
}