{"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/diffusion-stochastic-optimization-for-min-max","title":"Diffusion Stochastic Optimization for Min-Max Problems","arxiv_id":"2401.14585","date":"2024-01-26","proceeding":null,"authors":["Haoyuan Cai","Sulaiman A. Alghunaim","Ali H. Sayed"],"abstract":"The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional stochastic version suffers from the need for a large batch size on the order of $\\mathcal{O}(\\varepsilon^{-2})$ to achieve an $\\varepsilon$-stationary solution, we introduce and analyze a new formulation termed Diffusion Stochastic Same-Sample Optimistic Gradient (DSS-OG). We prove its convergence and resolve the large batch issue by establishing a tighter upper bound, under the more general setting of nonconvex Polyak-Lojasiewicz (PL) risk functions. We also extend the applicability of the proposed method to the distributed scenario, where agents communicate with their neighbors via a left-stochastic protocol. To implement DSS-OG, we can query the stochastic gradient oracles in parallel with some extra memory overhead, resulting in a complexity comparable to its conventional counterpart. To demonstrate the efficacy of the proposed algorithm, we conduct tests by training generative adversarial networks.","url_abs":"https://arxiv.org/abs/2401.14585v1","url_pdf":"https://arxiv.org/pdf/2401.14585v1.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":"diffusion-stochastic-optimization-for-min-max","repo_url":"https://github.com/mulgarfed/minimax_dssog","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}