Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games

2025-05-28

AI Summary

This work addresses the efficient computation of approximate Nash equilibria in ergodic mean-field games (MFGs) with finite state-action spaces. To this end, we propose Mean-Field Trust-Region Policy Optimization (MF-TRPO), the first algorithm systematically extending the trust-region stability mechanism of TRPO to the MFG setting. Theoretically, we establish the first finite-sample convergence bounds for MF-TRPO under both exact gradient and stochastic sampling settings, providing high-probability global convergence guarantees and explicit upper bounds on sample complexity. Technically, our analysis integrates mean-field approximation, stationary distribution analysis of Markov chains, and stochastic optimization theory. This work fills a critical theoretical gap—namely, trust-region–constrained policy optimization in MFGs—and significantly enhances the rigor and practicality of scalable multi-agent game solving.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Security and Privacy: Large-scale security measurements

Abstract

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting, we extend its methodology to the MFG framework, leveraging its stability and robustness in policy optimization. Under standard assumptions in the MFG literature, we provide a rigorous analysis of MF-TRPO, establishing theoretical guarantees on its convergence. Our results cover both the exact formulation of the algorithm and its sample-based counterpart, where we derive high-probability guarantees and finite sample complexity. This work advances MFG optimization by bridging RL techniques with mean-field decision-making, offering a theoretically grounded approach to solving complex multi-agent problems.

Problem

• Computes Nash equilibria for Mean-Field Games
• Extends TRPO to Mean-Field Game framework
• Provides convergence guarantees for MF-TRPO algorithm

Innovation

• Extends TRPO to Mean-Field Games
• Provides finite sample convergence guarantees
• Bridges RL with mean-field decision-making