Yilong Wan

Yilong Wan, Yuqiang Li, Xianyi Wu

We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria. This problem is crucial in high-stakes domains where online interaction is infeasible and adverse outcomes must be carefully controlled. However, existing literature on offline contextual bandits either centers on expected-reward criteria or restricts risk considerations to policy evaluation instead of optimization. In this work, we propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals, a broad class of risk measures encompassing mean-variance, entropic risk, and conditional value-at-risk, among others. By developing novel empirical concentration inequalities for importance sampling-based distributional estimators, our analysis derives data-dependent suboptimality bounds with an $\tilde{\mathcal{O}}(1/\sqrt{n})$ rate, without relying on restrictive uniform overlap assumptions. This rate is minimax optimal and matches that of risk-neutral offline policy optimization, indicating that optimizing general Lipschitz risk criteria incurs no additional statistical cost relative to the expected-reward.

Yilong Wan, Yuqiang Li, Xianyi Wu

This paper investigates off-policy evaluation in contextual bandits, aiming to quantify the performance of a target policy using data collected under a different and potentially unknown behavior policy. Recently, methods based on conformal prediction have been developed to construct reliable prediction intervals that guarantee marginal coverage in finite samples, making them particularly suited for safety-critical applications. To further achieve coverage conditional on a given offline data set, we propose a novel algorithm that constructs probably approximately correct prediction intervals. Our method builds upon a PAC-valid conformal prediction framework, and we strengthen its theoretical guarantees by establishing PAC-type bounds on coverage. We analyze both finite-sample and asymptotic properties of the proposed method, and compare its empirical performance with existing methods in simulations.