We study the problem of multi-agent reinforcement learning (MARL) with adaptivity constraints -- a new problem motivated by real-world applications where deployments of new policies are costly and the number of policy updates must be minimized. For two-player zero-sum Markov Games, we design a (policy) elimination based algorithm that achieves a regret of $\widetilde{O}(\sqrt{H^3 S^2 ABK})$, while the batch complexity is only $O(H+\log\log K)$. In the above, $S$ denotes the number of states, $A,B$ are the number of actions for the two players respectively, $H$ is the horizon and $K$ is the number of episodes. Furthermore, we prove a batch complexity lower bound $\Omega(\frac{H}{\log_{A}K}+\log\log K)$ for all algorithms with $\widetilde{O}(\sqrt{K})$ regret bound, which matches our upper bound up to logarithmic factors. As a byproduct, our techniques naturally extend to learning bandit games and reward-free MARL within near optimal batch complexity. To the best of our knowledge, these are the first line of results towards understanding MARL with low adaptivity.

多智能体强化学习中，通过引入自适应约束，我们设计一种基于消除的算法，在低批次复杂度下实现了对马尔可夫博弈的极小后悔，并且证明了匹配上界的批次复杂度下限，进一步地在理解低适应性的多智能体强化学习方面提供了首个一系列结果。

自适应约束下的自训练近最优强化学习