Scalable Primal-Dual Actor-Critic Method for Safe Multi-Agent RL with General Utilities

TL;DR

This paper introduces a scalable primal-dual actor-critic algorithm for safe multi-agent reinforcement learning with general utilities, addressing challenges of large state-action spaces and agent safety constraints.

Contribution

It proposes a novel primal-dual method with neighbor truncation for safe multi-agent RL under general utilities, with proven convergence and sample complexity guarantees.

Findings

Algorithm converges to a first-order stationary point at rate O(T^{-2/3})

Sample complexity is approximately O(ε^{-3.5}) for ε-approximate solutions

Numerical experiments demonstrate the method's effectiveness

Abstract

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and $\kappa$-hop neighbor truncation under a form of correlation decay property, where $\kappa$ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of $\mathcal{O}\left(T^{-2/3}\right)$. In the sample-based setting, we demonstrate that, with high probability, our algorithm requires $\widetilde{\mathcal{O}}\left(\epsilon^{-3.5}\right)$ samples to achieve an $\epsilon$-FOSP with an approximation error of $\mathcal{O}(\phi_0^{2\kappa})$, where $\phi_0\in (0,1)$. Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.