Christian Kroer, K. Waugh, F. Kılınç-Karzan, T. Sandholm
{"title":"广义博弈求解的快速一阶方法","authors":"Christian Kroer, K. Waugh, F. Kılınç-Karzan, T. Sandholm","doi":"10.1145/2764468.2764476","DOIUrl":null,"url":null,"abstract":"We study the problem of computing a Nash equilibrium in large-scale two-player zero-sum extensive-form games. While this problem can be solved in polynomial time, first-order or regret-based methods are usually preferred for large games. Regret-based methods have largely been favored in practice, in spite of their theoretically inferior convergence rates. In this paper we investigate the acceleration of first-order methods both theoretically and experimentally. An important component of many first-order methods is a distance-generating function. Motivated by this, we investigate a specific distance-generating function, namely the dilated entropy function, over treeplexes, which are convex polytopes that encompass the strategy spaces of perfect-recall extensive-form games. We develop significantly stronger bounds on the associated strong convexity parameter. In terms of extensive-form game solving, this improves the convergence rate of several first-order methods by a factor of O((#information sets ⋅ depth ⋅ M)/(2depth)) where M is the maximum value of the l1 norm over the treeplex encoding the strategy spaces. Experimentally, we investigate the performance of three first-order methods (the excessive gap technique, mirror prox, and stochastic mirror prox) and compare their performance to the regret-based algorithms. In order to instantiate stochastic mirror prox, we develop a class of gradient sampling schemes for game trees. Equipped with our distance-generating function and sampling scheme, we find that mirror prox and the excessive gap technique outperform the prior regret-based methods for finding medium accuracy solutions","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"49","resultStr":"{\"title\":\"Faster First-Order Methods for Extensive-Form Game Solving\",\"authors\":\"Christian Kroer, K. Waugh, F. Kılınç-Karzan, T. Sandholm\",\"doi\":\"10.1145/2764468.2764476\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the problem of computing a Nash equilibrium in large-scale two-player zero-sum extensive-form games. While this problem can be solved in polynomial time, first-order or regret-based methods are usually preferred for large games. Regret-based methods have largely been favored in practice, in spite of their theoretically inferior convergence rates. In this paper we investigate the acceleration of first-order methods both theoretically and experimentally. An important component of many first-order methods is a distance-generating function. Motivated by this, we investigate a specific distance-generating function, namely the dilated entropy function, over treeplexes, which are convex polytopes that encompass the strategy spaces of perfect-recall extensive-form games. We develop significantly stronger bounds on the associated strong convexity parameter. In terms of extensive-form game solving, this improves the convergence rate of several first-order methods by a factor of O((#information sets ⋅ depth ⋅ M)/(2depth)) where M is the maximum value of the l1 norm over the treeplex encoding the strategy spaces. Experimentally, we investigate the performance of three first-order methods (the excessive gap technique, mirror prox, and stochastic mirror prox) and compare their performance to the regret-based algorithms. In order to instantiate stochastic mirror prox, we develop a class of gradient sampling schemes for game trees. Equipped with our distance-generating function and sampling scheme, we find that mirror prox and the excessive gap technique outperform the prior regret-based methods for finding medium accuracy solutions\",\"PeriodicalId\":376992,\"journal\":{\"name\":\"Proceedings of the Sixteenth ACM Conference on Economics and Computation\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"49\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Sixteenth ACM Conference on Economics and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2764468.2764476\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2764468.2764476","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Faster First-Order Methods for Extensive-Form Game Solving
We study the problem of computing a Nash equilibrium in large-scale two-player zero-sum extensive-form games. While this problem can be solved in polynomial time, first-order or regret-based methods are usually preferred for large games. Regret-based methods have largely been favored in practice, in spite of their theoretically inferior convergence rates. In this paper we investigate the acceleration of first-order methods both theoretically and experimentally. An important component of many first-order methods is a distance-generating function. Motivated by this, we investigate a specific distance-generating function, namely the dilated entropy function, over treeplexes, which are convex polytopes that encompass the strategy spaces of perfect-recall extensive-form games. We develop significantly stronger bounds on the associated strong convexity parameter. In terms of extensive-form game solving, this improves the convergence rate of several first-order methods by a factor of O((#information sets ⋅ depth ⋅ M)/(2depth)) where M is the maximum value of the l1 norm over the treeplex encoding the strategy spaces. Experimentally, we investigate the performance of three first-order methods (the excessive gap technique, mirror prox, and stochastic mirror prox) and compare their performance to the regret-based algorithms. In order to instantiate stochastic mirror prox, we develop a class of gradient sampling schemes for game trees. Equipped with our distance-generating function and sampling scheme, we find that mirror prox and the excessive gap technique outperform the prior regret-based methods for finding medium accuracy solutions