Scalable Primal-Dual Actor-Critic Method for Safe Multi-Agent RL with General Utilities
This addresses scalable decision-making for multi-agent systems with safety and nonlinear objectives, but it is incremental as it builds on existing primal-dual and actor-critic frameworks.
The paper tackles safe multi-agent reinforcement learning with general utilities and safety constraints, proposing a primal-dual method that converges to a first-order stationary point at a rate of O(T^{-2/3}) in the exact setting and requires Õ(ε^{-3.5}) samples to achieve an ε-approximation in the sample-based setting.
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 $κ$-hop neighbor truncation under a form of correlation decay property, where $κ$ 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 $\widetilde{\mathcal{O}}\left(ε^{-3.5}\right)$ samples to achieve an $ε$-FOSP with an approximation error of $\mathcal{O}(φ_0^{2κ})$, where $φ_0\in (0,1)$. Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.