Safe Multi-Agent Reinforcement Learning with Convergence to Generalized Nash Equilibrium (2411.15036v1)

Abstract: Multi-agent reinforcement learning (MARL) has achieved notable success in cooperative tasks, demonstrating impressive performance and scalability. However, deploying MARL agents in real-world applications presents critical safety challenges. Current safe MARL algorithms are largely based on the constrained Markov decision process (CMDP) framework, which enforces constraints only on discounted cumulative costs and lacks an all-time safety assurance. Moreover, these methods often overlook the feasibility issue (the system will inevitably violate state constraints within certain regions of the constraint set), resulting in either suboptimal performance or increased constraint violations. To address these challenges, we propose a novel theoretical framework for safe MARL with $\textit{state-wise}$ constraints, where safety requirements are enforced at every state the agents visit. To resolve the feasibility issue, we leverage a control-theoretic notion of the feasible region, the controlled invariant set (CIS), characterized by the safety value function. We develop a multi-agent method for identifying CISs, ensuring convergence to a Nash equilibrium on the safety value function. By incorporating CIS identification into the learning process, we introduce a multi-agent dual policy iteration algorithm that guarantees convergence to a generalized Nash equilibrium in state-wise constrained cooperative Markov games, achieving an optimal balance between feasibility and performance. Furthermore, for practical deployment in complex high-dimensional systems, we propose $\textit{Multi-Agent Dual Actor-Critic}$ (MADAC), a safe MARL algorithm that approximates the proposed iteration scheme within the deep RL paradigm. Empirical evaluations on safe MARL benchmarks demonstrate that MADAC consistently outperforms existing methods, delivering much higher rewards while reducing constraint violations.

Insight into Safe Multi-Agent Reinforcement Learning with Convergence to Generalized Nash Equilibrium

This paper, authored by Zeyang Li and Navid Azizan from MIT, provides a comprehensive treatment of ensuring safety in multi-agent reinforcement learning (MARL) while maintaining performance. It emphasizes convergence to Generalized Nash Equilibria (GNE) in cooperative MARL settings marked by strict safety constraints.

The authors address several inherent challenges in deploying MARL in real-world scenarios. Key criticisms of current safe MARL methods include their reliance on the constrained Markov decision process (CMDP) framework, which only enforces constraints on expected cumulative rewards, a weakness under real-world demands for persistent safety. The paper introduces a novel framework focusing on state-wise constraints, ensuring that safety requirements are met at each visited state, which is pertinent for environments such as autonomous driving, where consistent adherence to constraints is critical.

Central to the proposed framework is the identification of Controlled Invariant Sets (CIS) through a control-theoretic approach. CIS are leveraged to ensure that any region marked as safe can be preserved by following certain policies, preventing the system from inadvertently breaching constraints. By utilizing the safety value function derived from Hamilton-Jacobi reachability analysis, the paper introduces a method to safely navigate these environments while achieving policy convergence to Nash equilibrium.

A significant advancement in this work is the introduction of the Multi-Agent Dual Policy Iteration algorithm. This approach coordinates agent actions within state-wise constrained cooperative Markov games, ensuring convergence to GNE. A notable feature of this algorithm is its ability to strike a balance between maximizing performance and satisfying safety constraints, even amidst the non-stationarity challenges typical of multi-agent environments. The formulation effectively transforms state constraints into action-space constraints, facilitating optimization across feasible directions.

Beyond theoretical contributions, the paper delivers practical outcomes through the development of Multi-Agent Dual Actor-Critic (MADAC) within deep reinforcement learning paradigms. Empirical results demonstrate MADAC's effectiveness on challenging high-dimensional benchmarks, consistently outperforming existing methods. For instance, MADAC showcases its ability to achieve higher rewards while reducing constraint violations, standing out in performance compared to state-of-the-art safe MARL baselines such as MACPO and MAPPO-Lagrangian.

The implications of this work are notable for both researchers and practitioners. Theoretically, it provides new insights into leveraging CIS for safety guarantees in MARL, addressing feasibility challenges that previous works often overlook. Practically, the robustness of MADAC suggests its potential applicability in complex, real-world systems where safety is paramount. Future research could extend this framework to even more complex settings, exploring scalability and adaptability in dynamically changing environments.

In conclusion, the paper significantly contributes to the safety-preserving landscape of MARL, offering a methodological and algorithmic strategy that is both practically and theoretically significant. By ensuring that convergence aligns with GNE within safety constraints, it sets a precedent for future research and deployment of MARL in safety-critical applications.