  We investigate the problem of corruption robustness in offline reinforcement
learning (RL) with general function approximation, where an adversary can
corrupt each sample in the offline dataset, and the corruption level
$\zeta\geq0$ quantifies the cumulative corruption amount over $n$ episodes and
$H$ steps. Our goal is to find a policy that is robust to such corruption and
minimizes the suboptimality gap with respect to the optimal policy for the
uncorrupted Markov decision processes (MDPs). Drawing inspiration from the
uncertainty-weighting technique from the robust online RL setting
\citep{he2022nearly,ye2022corruptionrobust}, we design a new uncertainty weight
iteration procedure to efficiently compute on batched samples and propose a
corruption-robust algorithm for offline RL. Notably, under the assumption of
single policy coverage and the knowledge of $\zeta$, our proposed algorithm
achieves a suboptimality bound that is worsened by an additive factor of
$\mathcal{O}(\zeta (C(\widehat{\mathcal{F}},\mu)n)^{-1})$ due to the
corruption. Here $\widehat{\mathcal{F}}$ is the confidence set, and the dataset
$\mathcal{Z}_n^H$, and $C(\widehat{\mathcal{F}},\mu)$ is a coefficient that
depends on $\widehat{\mathcal{F}}$ and the underlying data distribution $\mu$.
When specialized to linear MDPs, the corruption-dependent error term reduces to
$\mathcal{O}(\zeta d n^{-1})$ with $d$ being the dimension of the feature map,
which matches the existing lower bound for corrupted linear MDPs. This suggests
that our analysis is tight in terms of the corruption-dependent term.
