勷勤数学•专家报告

题      目：Continuous-time reinforcement learning for mean-field game and mean-field control problems

报  告  人：魏晓利 副教授  (邀请人：杨舟)

                                   哈尔滨工业大学

时      间：4月29日  15：00-16：00

地     点：数科院西楼二楼会议室

报告人简介:

       魏晓利，哈尔滨工业大学副教授(准聘)。本科毕业于中国科学技术大学，2018年于巴黎第七大学获得博士学位。2019-2021年在加州大学伯克利分校从事博士后。2021年-2023年就职于清华大学深圳国际研究生院。主要从事随机微分博弈、强化学习等研究。论文发表在Operations Research， Mathematical Finance, SIAM Journal on Control and Optimization等期刊杂志。

摘      要：

      We study the continuous-time q-learning in mean-field models when the population distribution is not directly observable. We propose the integrated q-function in decoupled form (decoupled Iq-function) from the representative agent's perspective and establish its martingale characterization, which provides a unified policy evaluation rule for both mean-field game (MFG) and mean-field control (MFC) problems. Moreover, we consider the learning procedure where the representative agent updates the population distribution based on his own state values. Depending on the task to solve the MFG or MFC problem, we can employ the decoupled Iq-function differently to characterize the mean-field equilibrium policy or the mean-field optimal policy respectively. Based on these theoretical findings, we devise a unified q-learning algorithm for both MFG and MFC problems by utilizing test policies and the averaged martingale orthogonality condition. Finally, we illustrate our q-learning algorithm with financial examples.

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