{"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/the-mechanics-of-n-player-differentiable","title":"The Mechanics of n-Player Differentiable Games","arxiv_id":"1802.05642","date":"2018-02-15","proceeding":"ICML 2018 7","authors":["David Balduzzi","Sebastien Racaniere","James Martens","Jakob Foerster","Karl Tuyls","Thore Graepel"],"abstract":"The cornerstone underpinning deep learning is the guarantee that gradient\ndescent on an objective converges to local minima. Unfortunately, this\nguarantee fails in settings, such as generative adversarial nets, where there\nare multiple interacting losses. The behavior of gradient-based methods in\ngames is not well understood -- and is becoming increasingly important as\nadversarial and multi-objective architectures proliferate. In this paper, we\ndevelop new techniques to understand and control the dynamics in general games.\nThe key result is to decompose the second-order dynamics into two components.\nThe first is related to potential games, which reduce to gradient descent on an\nimplicit function; the second relates to Hamiltonian games, a new class of\ngames that obey a conservation law, akin to conservation laws in classical\nmechanical systems. The decomposition motivates Symplectic Gradient Adjustment\n(SGA), a new algorithm for finding stable fixed points in general games. Basic\nexperiments show SGA is competitive with recently proposed algorithms for\nfinding stable fixed points in GANs -- whilst at the same time being applicable\nto -- and having guarantees in -- much more general games.","url_abs":"http://arxiv.org/abs/1802.05642v2","url_pdf":"http://arxiv.org/pdf/1802.05642v2.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":"the-mechanics-of-n-player-differentiable","repo_url":"https://github.com/deepmind/symplectic-gradient-adjustment","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.05642","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}