{"title":"在潜在均值场博弈中学习最优策略：平滑政策迭代算法","authors":"Qing Tang, Jiahao Song","doi":"10.1137/22m1539861","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 351-375, February 2024. <br/> Abstract. We introduce two smoothed policy iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential mean field games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfies the Lasry–Lions monotonicity condition. Local convergence to a stable solution is proved for a system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the fictitious play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms\",\"authors\":\"Qing Tang, Jiahao Song\",\"doi\":\"10.1137/22m1539861\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 351-375, February 2024. <br/> Abstract. We introduce two smoothed policy iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential mean field games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfies the Lasry–Lions monotonicity condition. Local convergence to a stable solution is proved for a system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the fictitious play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Control and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1539861\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1539861","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 351-375, February 2024. Abstract. We introduce two smoothed policy iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential mean field games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfies the Lasry–Lions monotonicity condition. Local convergence to a stable solution is proved for a system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the fictitious play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.
期刊介绍：
SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition.
The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.
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