This paper considers multi-agent reinforcement learning (MARL) where the rewards are received after delays and the delay time varies across agents and across time steps. 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 total delay formally defined in the paper. Moreover, our algorithm is extended to cases with infinite delays through a reward skipping scheme. It achieves convergence rate similar to the finite delay case.

翻译：本文考虑多智能体强化学习（MARL），其中奖励在延迟后收到，且延迟时间因智能体和时间步长而异。基于V学习框架，本文提出了有效处理奖励延迟的MARL算法。当延迟有限时，我们的算法以速率$\tilde{\mathcal{O}}(\frac{H^3\sqrt{S\mathcal{T}_K}}{K}+\frac{H^3\sqrt{SA}}{\sqrt{K}})$达到粗相关均衡（CCE），其中$K$为回合数，$H$为规划视界，$S$为状态空间大小，$A$为最大动作空间大小，$\mathcal{T}_K$为论文中正式定义的总延迟度量。此外，通过奖励跳过方案，我们的算法可扩展到无穷延迟情况，其收敛速率与有限延迟情形相似。