Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games
This work addresses complex multi-agent decision-making problems in mean-field games, offering a theoretically grounded optimization approach, though it is incremental as it adapts an existing RL method to a new framework.
The paper tackled computing approximate Nash equilibria for ergodic Mean-Field Games by introducing MF-TRPO, an algorithm extending TRPO to this setting, and provided theoretical convergence guarantees and finite sample complexity bounds.
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.