Pessimistic Risk-Aware Policy Learning in Contextual Bandits

• URL: http://arxiv.org/abs/2605.15620v1
• Date: Fri, 15 May 2026 05:02:39 GMT
• Title: Pessimistic Risk-Aware Policy Learning in Contextual Bandits
• Abstract summary: We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria.<n>We propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals.
• Score: 3.085723806353297
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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