Model Selection in Batch Policy Optimization
This addresses the problem of selecting optimal models in batch policy optimization for researchers and practitioners in reinforcement learning, though it is incremental as it builds on existing supervised learning methods while highlighting unique challenges in the batch setting.
The paper tackles model selection in batch policy optimization by identifying three error sources—approximation error, statistical complexity, and coverage—and shows that no algorithm can address all three simultaneously, but relaxing any one enables near-oracle performance for the others, with experiments validating these algorithms.
We study the problem of model selection in batch policy optimization: given a fixed, partial-feedback dataset and $M$ model classes, learn a policy with performance that is competitive with the policy derived from the best model class. We formalize the problem in the contextual bandit setting with linear model classes by identifying three sources of error that any model selection algorithm should optimally trade-off in order to be competitive: (1) approximation error, (2) statistical complexity, and (3) coverage. The first two sources are common in model selection for supervised learning, where optimally trading-off these properties is well-studied. In contrast, the third source is unique to batch policy optimization and is due to dataset shift inherent to the setting. We first show that no batch policy optimization algorithm can achieve a guarantee addressing all three simultaneously, revealing a stark contrast between difficulties in batch policy optimization and the positive results available in supervised learning. Despite this negative result, we show that relaxing any one of the three error sources enables the design of algorithms achieving near-oracle inequalities for the remaining two. We conclude with experiments demonstrating the efficacy of these algorithms.