Sample and Communication Efficient Fully Decentralized MARL Policy Evaluation via a New Approach: Local TD update

In actor-critic framework for fully decentralized multi-agent reinforcement learning (MARL), one of the key components is the MARL policy evaluation (PE) problem, where a set of N agents work cooperatively to evaluate the value function of the global states for a given policy through communicating with their neighbors. In MARL-PE, a critical challenge is how to lower the sample and communication complexities, which are defined as the number of training samples and communication rounds needed to converge to some ε-stationary point. To lower communication complexity in MARL-PE, a "natural'' idea is to perform multiple local TD-update steps between each consecutive rounds of communication to reduce the communication frequency. However, the validity of the local TD-update approach remains unclear due to the potential "agent-drift'' phenomenon resulting from heterogeneous rewards across agents in general. This leads to an interesting open question: Can the local TD-update approach entail low sample and communication complexities? In this paper, we make the first attempt to answer this fundamental question. We focus on the setting of MARL-PE with average reward, which is motivated by many multi-agent network optimization problems. Our theoretical and experimental results confirm that allowing multiple local TD-update steps is indeed an effective approach in lowering the sample and communication complexities of MARL-PE compared to consensus-based MARL-PE algorithms. Specifically, the local TD-update steps between two consecutive communication rounds can be as large as O(1/ε1/2log(1/ε)) in order to converge to an ε-stationary point of MARL-PE. Moreover, we show theoretically that in order to reach the optimal sample complexity, the communication complexity of local TD-update approach is O(1/ε1/2log(1/ε)).