Title: Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage. Abstract: We study model-based offline Reinforcement Learning with general function approximation without a full coverage assumption on the offline data distribution. We present an algorithm named Constrained Pessimistic Policy Optimization (CPPO) which leverages a general function class and uses a constraint over the models to encode pessimism. Under the assumption that the ground truth model belongs to our function class (i.e., realizability in the function class), CPPO has a PAC guarantee with offline data only providing partial coverage, i.e., it can learn a policy that competes against any policy covered by the offline data. We then demonstrate that this algorithmic framework can be applied to many specialized Markov Decision Processes where the additional structural assumptions can further refine the concept of partial coverage. Two notable examples are: (1) low- rank MDP with representation learning where the partial coverage condition is defined using a relative condition number measured by the unknown ground truth feature representation; (2) factored MDP where the partial coverage condition is defined using density-ratio based concentrability coefficients associated with individual factors.