  This paper considers offline multi-agent reinforcement learning. We propose
the strategy-wise concentration principle which directly builds a confidence
interval for the joint strategy, in contrast to the point-wise concentration
principle that builds a confidence interval for each point in the joint action
space. For two-player zero-sum Markov games, by exploiting the convexity of the
strategy-wise bonus, we propose a computationally efficient algorithm whose
sample complexity enjoys a better dependency on the number of actions than the
prior methods based on the point-wise bonus. Furthermore, for offline
multi-agent general-sum Markov games, based on the strategy-wise bonus and a
novel surrogate function, we give the first algorithm whose sample complexity
only scales $\sum_{i=1}^mA_i$ where $A_i$ is the action size of the $i$-th
player and $m$ is the number of players. In sharp contrast, the sample
complexity of methods based on the point-wise bonus would scale with the size
of the joint action space $\Pi_{i=1}^m A_i$ due to the curse of multiagents.
Lastly, all of our algorithms can naturally take a pre-specified strategy class
$\Pi$ as input and output a strategy that is close to the best strategy in
$\Pi$. In this setting, the sample complexity only scales with $\log |\Pi|$
instead of $\sum_{i=1}^mA_i$.
