  Offline multi-agent reinforcement learning is challenging due to the coupling
effect of both distribution shift issue common in offline setting and the high
dimension issue common in multi-agent setting, making the action
out-of-distribution (OOD) and value overestimation phenomenon excessively
severe. Tomitigate this problem, we propose a novel multi-agent offline RL
algorithm, named CounterFactual Conservative Q-Learning (CFCQL) to conduct
conservative value estimation. Rather than regarding all the agents as a high
dimensional single one and directly applying single agent methods to it, CFCQL
calculates conservative regularization for each agent separately in a
counterfactual way and then linearly combines them to realize an overall
conservative value estimation. We prove that it still enjoys the
underestimation property and the performance guarantee as those single agent
conservative methods do, but the induced regularization and safe policy
improvement bound are independent of the agent number, which is therefore
theoretically superior to the direct treatment referred to above, especially
when the agent number is large. We further conduct experiments on four
environments including both discrete and continuous action settings on both
existing and our man-made datasets, demonstrating that CFCQL outperforms
existing methods on most datasets and even with a remarkable margin on some of
them.
