{"type":"ScholarlyArticle","title":"Finding Mixed-Strategy Equilibria of Continuous-Action Games without Gradients Using Randomized Policy Networks","authors":[{"name":"Carlos Martin","slug":"carlos-martin","given":"Carlos","family":"Martin","affiliation":"Carnegie Mellon University"},{"name":"Tuomas Sandholm","slug":"tuomas-sandholm","given":"Tuomas","family":"Sandholm","affiliation":"Carnegie Mellon University; Strategy Robot, Inc.; Optimized Markets, Inc.; Strategic Machine, Inc."}],"abstract":"We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black box. To tackle this problem, we apply zeroth-order optimization techniques that combine smoothed gradient estimators with equilibrium-finding dynamics.\r\nWe model players' strategies using artificial neural networks. In particular, we use randomized policy networks to model mixed strategies. These take noise in addition to an observation as input and can flexibly represent arbitrary observation-dependent, continuous-action distributions. Being able to model such mixed strategies is crucial for tackling continuous-action games that lack pure-strategy equilibria.\r\nWe evaluate the performance of our method using an approximation of the Nash convergence metric from game theory, which measures how much players can benefit from unilaterally changing their strategy.\r\nWe apply our method to continuous Colonel Blotto games, single-item and multi-item auctions, and a visibility game.\r\nThe experiments show that our method can quickly find a high-quality approximate equilibrium.\r\nFurthermore, they show that the dimensionality of the input noise is crucial for performance.\r\nTo our knowledge, this paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.","doi":"10.24963/ijcai.2023/317","url":"https://ijcai.org/proceedings/2023/317","pdf":"https://ijcai.org/proceedings/2023/0317.pdf","markdown":"https://ijcai.org/proceedings/2023/317.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/317","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":317,"pages":{"first":2844,"last":2852},"keywords":["Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[Adam et al., 2021] Lukáš Adam, Rostislav Horčík, Tomáš Kasl, and Tomáš Kroupa. 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