Offline Policy Selection under Uncertainty

The presence of uncertainty in policy evaluation significantly complicates the process of policy ranking and selection in real-world settings. We formally consider offline policy selection as learning preferences over a set of policy prospects given a fixed experience dataset. While one can select or rank policies based on point estimates of their expected values or high-confidence intervals, access to the full distribution over one's belief of the policy value enables more flexible selection algorithms under a wider range of downstream evaluation metrics. We propose a Bayesian approach for estimating this belief distribution in terms of posteriors of distribution correction ratios derived from stochastic constraints. Empirically, despite being Bayesian, the credible intervals obtained are competitive with state-of-the-art frequentist approaches in confidence interval estimation. More importantly, we show how the belief distribution may be used to rank policies with respect to arbitrary downstream policy selection metrics, and empirically demonstrate that this selection procedure significantly outperforms existing approaches, such as ranking policies according to mean or high-confidence lower bound value estimates.