Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage
This addresses the problem of limited data coverage in offline RL for researchers and practitioners, offering a theoretical framework with applications to specialized MDPs, though it is incremental in refining coverage conditions.
The paper tackles offline reinforcement learning with partial data coverage by proposing Constrained Pessimistic Policy Optimization (CPPO), which achieves a PAC guarantee to learn policies competitive with any covered policy under realizability assumptions.
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 model class 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 that is covered by the offline data. We then demonstrate that this algorithmic framework can be applied to many specialized Markov Decision Processes where 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.