[Paper Review] A Game-Theoretic Approach to Multi-Agent Trust Region Optimization

Ying Wen, Hui Chen+5 more|arXiv (Cornell University)|Jun 12, 2021

Reinforcement Learning in Robotics70 references4 citations

TL;DR

This paper proposes MATRL, a game-theoretic multi-agent trust region learning method that integrates meta-game analysis to stabilize policy optimization in nonstationary multi-agent environments. By leveraging Nash equilibrium solutions in an empirical policy-space meta-game, MATRL ensures monotonic performance improvement and local convergence, outperforming strong baselines in discrete and continuous control tasks including MuJoCo and Atari games.

ABSTRACT

Trust region methods are widely applied in single-agent reinforcement learning problems due to their monotonic performance-improvement guarantee at every iteration. Nonetheless, when applied in multi-agent settings, the guarantee of trust region methods no longer holds because an agent's payoff is also affected by other agents' adaptive behaviors. To tackle this problem, we conduct a game-theoretical analysis in the policy space, and propose a multi-agent trust region learning method (MATRL), which enables trust region optimization for multi-agent learning. Specifically, MATRL finds a stable improvement direction that is guided by the solution concept of Nash equilibrium at the meta-game level. We derive the monotonic improvement guarantee in multi-agent settings and empirically show the local convergence of MATRL to stable fixed points in the two-player rotational differential game. To test our method, we evaluate MATRL in both discrete and continuous multiplayer general-sum games including checker and switch grid worlds, multi-agent MuJoCo, and Atari games. Results suggest that MATRL significantly outperforms strong multi-agent reinforcement learning baselines.

Motivation & Objective

• To address the breakdown of trust region monotonic improvement in multi-agent settings due to nonstationary environments caused by other agents' adaptive behaviors.
• To develop a trust region method that maintains performance guarantees in multi-agent reinforcement learning without requiring centralized critics or communication.
• To enable convergence to stable fixed points via meta-game analysis using Nash equilibrium concepts in the policy space.
• To improve learning stability and sample efficiency in general-sum multi-agent environments while retaining the simplicity of independent learners.
• To provide a minimal-overhead extension to existing trust region algorithms like PPO, avoiding additional training or architectural changes.

Proposed method

• Construct an empirical policy-space meta-game using current and predicted policies from independent learners (ILs) to model joint payoff dynamics.
• Use a Nash equilibrium solver (e.g., CMAES) to identify stable policy updates in the meta-game, ensuring weak stability in the underlying game.
• Aggregate current and predicted policies via the meta-game Nash equilibrium to define a restricted trust region step.
• Apply best response updates based on the aggregated policy to explore stable directions, improving robustness to policy shifts.
• Integrate the meta-game analysis into standard trust region algorithms (e.g., PPO) without modifying the underlying policy or value networks.
• Maintain the original PPO loss with added KL and entropy regularization, while introducing best response learning steps to refine policy updates.

Experimental results

Research questions

• RQ1 Can trust region optimization maintain monotonic performance improvement in multi-agent settings despite nonstationary environments?
• RQ2 Does incorporating a meta-game Nash equilibrium in policy space lead to stable and convergent learning in multi-agent reinforcement learning?
• RQ3 Can a minimal-overhead extension to independent learners achieve performance comparable to centralized or communication-based methods?
• RQ4 How does the proposed method compare to strong baselines like VDN, QMIX, MADDPG, and COMIX in discrete and continuous control environments?
• RQ5 Is the meta-game Nash equilibrium a weak stable fixed point of the underlying multi-agent game?

Key findings

• MATRL achieves significant performance gains over independent PPO, VDN, QMIX, and QDPP in discrete grid-world environments such as 2-player switch and checker games.
• In continuous control tasks using multi-agent MuJoCo, MATRL outperforms decentralized PPO, MADDPG, and COMIX, demonstrating superior sample efficiency and stability.
• In zero-sum Atari games, MATRL surpasses the baseline PPO and centralized methods like COMIX, achieving higher final returns with consistent learning curves.
• The method ensures monotonic improvement in expected returns across training iterations, validating the theoretical guarantee under meta-game analysis.
• Local convergence to stable fixed points is empirically observed in differential game dynamics, supporting the theoretical analysis of weak stability.
• The use of CMAES for Nash equilibrium solving in the meta-game enables effective and scalable trust region updates without centralized infrastructure.