  We study offline reinforcement learning (RL) in partially observable Markov
decision processes. In particular, we aim to learn an optimal policy from a
dataset collected by a behavior policy which possibly depends on the latent
state. Such a dataset is confounded in the sense that the latent state
simultaneously affects the action and the observation, which is prohibitive for
existing offline RL algorithms. To this end, we propose the \underline{P}roxy
variable \underline{P}essimistic \underline{P}olicy \underline{O}ptimization
(\texttt{P3O}) algorithm, which addresses the confounding bias and the
distributional shift between the optimal and behavior policies in the context
of general function approximation. At the core of \texttt{P3O} is a coupled
sequence of pessimistic confidence regions constructed via proximal causal
inference, which is formulated as minimax estimation. Under a partial coverage
assumption on the confounded dataset, we prove that \texttt{P3O} achieves a
$n^{-1/2}$-suboptimality, where $n$ is the number of trajectories in the
dataset. To our best knowledge, \texttt{P3O} is the first provably efficient
offline RL algorithm for POMDPs with a confounded dataset.
