Multi-Agent Reinforcement Learning with Reward Delays

This paper considers multi-agent reinforcement learning (MARL) where the rewards are received after delays and the delay time varies among agents. Based on the V-learning framework, this paper proposes MARL algorithms that efficiently deal with reward delays. When the delays are finite, our algorithm reaches a coarse correlated equilibrium (CCE) with rate $\tilde{\mathcal{O}}(\frac{H^3\sqrt{S\mathcal{T}_K}}{K}+\frac{H^3\sqrt{SA}}{\sqrt{K}})$ where $K$ is the number of episodes, $H$ is the planning horizon, $S$ is the size of the state space, $A$ is the size of the largest action space, and $\mathcal{T}_K$ is the measure of the total delay defined in the paper. Moreover, our algorithm can be extended to cases with infinite delays through a reward skipping scheme. It achieves convergence rate similar to the finite delay case.