When is Offline Policy Selection Sample Efficient for Reinforcement Learning?

Offline reinforcement learning algorithms often require careful hyperparameter tuning. Consequently, before deployment, we need to select amongst a set of candidate policies. As yet, however, there is little understanding about the fundamental limits of this offline policy selection (OPS) problem. In this work we aim to provide clarity on when sample efficient OPS is possible, primarily by connecting OPS to off-policy policy evaluation (OPE) and Bellman error (BE) estimation. We first show a hardness result, that in the worst case, OPS is just as hard as OPE, by proving a reduction of OPE to OPS. As a result, no OPS method can be more sample efficient than OPE in the worst case. We then propose a BE method for OPS, called Identifiable BE Selection (IBES), that has a straightforward method for selecting its own hyperparameters. We highlight that using IBES for OPS generally has more requirements than OPE methods, but if satisfied, can be more sample efficient. We conclude with an empirical study comparing OPE and IBES, and by showing the difficulty of OPS on an offline Atari benchmark dataset.