Finite-Time Global Optimality Convergence in Deep Neural Actor-Critic Methods for Decentralized Multi-Agent Reinforcement Learning

Actor-critic methods for decentralized multi-agent reinforcement learning (MARL) facilitate collaborative optimal decision making without centralized coordination, thus enabling a wide range of applications in practice. To date, however, most theoretical convergence studies for existing actorcritic decentralized MARL methods are limited to the guarantee of a stationary solution under the linear function approximation. This leaves a significant gap between the highly successful use of deep neural actor-critic for decentralized MARL in practice and the current theoretical understanding. To bridge this gap, in this paper, we make the first attempt to develop a deep neural actor-critic method for decentralized MARL, where both the actor and critic components are inherently non-linear. We show that our proposed method enjoys a global optimality guarantee with a finite-time convergence rate of O(1/T ), where T is the total iteration times. This marks the first global convergence result for deep neural actorcritic methods in the MARL literature. We also conduct extensive numerical experiments, which verify our theoretical results.