逆均值场博弈的策略迭代法

Kui Ren, Nathan Soedjak, Shanyin Tong
{"title":"逆均值场博弈的策略迭代法","authors":"Kui Ren, Nathan Soedjak, Shanyin Tong","doi":"arxiv-2409.06184","DOIUrl":null,"url":null,"abstract":"We propose a policy iteration method to solve an inverse problem for a\nmean-field game model, specifically to reconstruct the obstacle function in the\ngame from the partial observation data of value functions, which represent the\noptimal costs for agents. The proposed approach decouples this complex inverse\nproblem, which is an optimization problem constrained by a coupled nonlinear\nforward and backward PDE system in the MFG, into several iterations of solving\nlinear PDEs and linear inverse problems. This method can also be viewed as a\nfixed-point iteration that simultaneously solves the MFG system and inversion.\nWe further prove its linear rate of convergence. In addition, numerical\nexamples in 1D and 2D, along with performance comparisons to a direct\nleast-squares method, demonstrate the superior efficiency and accuracy of the\nproposed method for solving inverse MFGs.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Policy Iteration Method for Inverse Mean Field Games\",\"authors\":\"Kui Ren, Nathan Soedjak, Shanyin Tong\",\"doi\":\"arxiv-2409.06184\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a policy iteration method to solve an inverse problem for a\\nmean-field game model, specifically to reconstruct the obstacle function in the\\ngame from the partial observation data of value functions, which represent the\\noptimal costs for agents. The proposed approach decouples this complex inverse\\nproblem, which is an optimization problem constrained by a coupled nonlinear\\nforward and backward PDE system in the MFG, into several iterations of solving\\nlinear PDEs and linear inverse problems. This method can also be viewed as a\\nfixed-point iteration that simultaneously solves the MFG system and inversion.\\nWe further prove its linear rate of convergence. In addition, numerical\\nexamples in 1D and 2D, along with performance comparisons to a direct\\nleast-squares method, demonstrate the superior efficiency and accuracy of the\\nproposed method for solving inverse MFGs.\",\"PeriodicalId\":501286,\"journal\":{\"name\":\"arXiv - MATH - Optimization and Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Optimization and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06184\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Optimization and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06184","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们提出了一种策略迭代方法来解决均场博弈模型的逆问题,具体来说,就是从价值函数的部分观测数据重建博弈中的障碍函数,而价值函数代表了代理的最优成本。所提出的方法将这个复杂的逆问题(即受 MFG 中耦合非线性前向和后向 PDE 系统约束的优化问题)解耦为求解线性 PDE 和线性逆问题的多次迭代。我们进一步证明了该方法的线性收敛速率。此外,一维和二维的数值示例,以及与直接最小二乘法的性能比较,都证明了所提方法在求解反 MFG 方面的卓越效率和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Policy Iteration Method for Inverse Mean Field Games
We propose a policy iteration method to solve an inverse problem for a mean-field game model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the optimal costs for agents. The proposed approach decouples this complex inverse problem, which is an optimization problem constrained by a coupled nonlinear forward and backward PDE system in the MFG, into several iterations of solving linear PDEs and linear inverse problems. This method can also be viewed as a fixed-point iteration that simultaneously solves the MFG system and inversion. We further prove its linear rate of convergence. In addition, numerical examples in 1D and 2D, along with performance comparisons to a direct least-squares method, demonstrate the superior efficiency and accuracy of the proposed method for solving inverse MFGs.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信