{"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/optimization-with-non-differentiable","title":"Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals","arxiv_id":"1809.04198","date":"2018-09-11","proceeding":null,"authors":["Andrew Cotter","Heinrich Jiang","Serena Wang","Taman Narayan","Maya Gupta","Seungil You","Karthik Sridharan"],"abstract":"We show that many machine learning goals, such as improved fairness metrics,\ncan be expressed as constraints on the model's predictions, which we call rate\nconstraints. We study the problem of training non-convex models subject to\nthese rate constraints (or any non-convex and non-differentiable constraints).\nIn the non-convex setting, the standard approach of Lagrange multipliers may\nfail. Furthermore, if the constraints are non-differentiable, then one cannot\noptimize the Lagrangian with gradient-based methods. To solve these issues, we\nintroduce the proxy-Lagrangian formulation. This new formulation leads to an\nalgorithm that produces a stochastic classifier by playing a two-player\nnon-zero-sum game solving for what we call a semi-coarse correlated\nequilibrium, which in turn corresponds to an approximately optimal and feasible\nsolution to the constrained optimization problem. We then give a procedure\nwhich shrinks the randomized solution down to one that is a mixture of at most\n$m+1$ deterministic solutions, given $m$ constraints. This culminates in\nalgorithms that can solve non-convex constrained optimization problems with\npossibly non-differentiable and non-convex constraints with theoretical\nguarantees. We provide extensive experimental results enforcing a wide range of\npolicy goals including different fairness metrics, and other goals on accuracy,\ncoverage, recall, and churn.","url_abs":"http://arxiv.org/abs/1809.04198v1","url_pdf":"http://arxiv.org/pdf/1809.04198v1.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":"optimization-with-non-differentiable","repo_url":"https://github.com/tensorflow/tensorflow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"2d-cyclist-detection","task_name":"2D Cyclist Detection"},{"task_slug":"fairness","task_name":"Fairness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1809.04198","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}