重构均值场博弈模型中与状态无关的成本函数

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-09-05 DOI:10.1088/1361-6420/ad7497

Kui Ren, Nathan Soedjak, Kewei Wang, Hongyu Zhai

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引用次数: 0

摘要

在这篇短文中，我们考虑了均场博弈（MFGs）系统的逆问题，我们感兴趣的是如何从观测到的价值函数数据中重建与状态无关的运行成本函数。我们使用标准的多线性化技术为逆问题的唯一性结果提供了一个基本证明。我们工作的主要特点之一是，我们坚持认为人口分布是一个概率度量，而现有的一些关于理论逆 MFGs 的文献并没有强制执行这一要求。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Reconstructing a state-independent cost function in a mean-field game model

In this short note, we consider an inverse problem to a mean-field games (MFGs) system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a uniqueness result for the inverse problem using the standard multilinearization technique. One of the main features of our work is that we insist that the population distribution be a probability measure, a requirement that is not enforced in some of the existing literature on theoretical inverse MFGs.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.