{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/two-player-games-for-efficient-non-convex","title":"Two-Player Games for Efficient Non-Convex Constrained Optimization","arxiv_id":"1804.06500","date":"2018-04-17","proceeding":null,"authors":["Andrew Cotter","Heinrich Jiang","Karthik Sridharan"],"abstract":"In recent years, constrained optimization has become increasingly relevant to\nthe machine learning community, with applications including Neyman-Pearson\nclassification, robust optimization, and fair machine learning. A natural\napproach to constrained optimization is to optimize the Lagrangian, but this is\nnot guaranteed to work in the non-convex setting, and, if using a first-order\nmethod, cannot cope with non-differentiable constraints (e.g. constraints on\nrates or proportions).\n  The Lagrangian can be interpreted as a two-player game played between a\nplayer who seeks to optimize over the model parameters, and a player who wishes\nto maximize over the Lagrange multipliers. We propose a non-zero-sum variant of\nthe Lagrangian formulation that can cope with non-differentiable--even\ndiscontinuous--constraints, which we call the \"proxy-Lagrangian\". The first\nplayer minimizes external regret in terms of easy-to-optimize \"proxy\nconstraints\", while the second player enforces the original constraints by\nminimizing swap regret.\n  For this new formulation, as for the Lagrangian in the non-convex setting,\nthe result is a stochastic classifier. For both the proxy-Lagrangian and\nLagrangian formulations, however, we prove that this classifier, instead of\nhaving unbounded size, can be taken to be a distribution over no more than m+1\nmodels (where m is the number of constraints). This is a significant\nimprovement in practical terms.","url_abs":"http://arxiv.org/abs/1804.06500v2","url_pdf":"http://arxiv.org/pdf/1804.06500v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"two-player-games-for-efficient-non-convex","repo_url":"https://github.com/google-research/tensorflow_constrained_optimization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1804.06500","atlas_url":"https://app.syntology.ai/?focus=1804.06500","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}