Analysis of Multiscale Reinforcement Q-Learning Algorithms for Mean Field Control Games

Autor:	Angiuli, Andrea, Fouque, Jean-Pierre, Laurière, Mathieu, Zhang, Mengrui
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Computer Science - Machine Learning Computer Science - Multiagent Systems
Druh dokumentu:	Working Paper
Popis:	Mean Field Control Games (MFCG), introduced in [Angiuli et al., 2022a], represent competitive games between a large number of large collaborative groups of agents in the infinite limit of number and size of groups. In this paper, we prove the convergence of a three-timescale Reinforcement Q-Learning (RL) algorithm to solve MFCG in a model-free approach from the point of view of representative agents. Our analysis uses a Q-table for finite state and action spaces updated at each discrete time-step over an infinite horizon. In [Angiuli et al., 2023], we proved convergence of two-timescale algorithms for MFG and MFC separately highlighting the need to follow multiple population distributions in the MFC case. Here, we integrate this feature for MFCG as well as three rates of update decreasing to zero in the proper ratios. Our technique of proof uses a generalization to three timescales of the two-timescale analysis in [Borkar, 1997]. We give a simple example satisfying the various hypothesis made in the proof of convergence and illustrating the performance of the algorithm. Comment: arXiv admin note: text overlap with arXiv:2312.06659
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.17017 Zobrazit plný text záznamu View this record from Arxiv