Mitigating PROWL’s conservatism under one-sided validity

Develop methods that reduce the finite-sample conservatism of PAC-Bayesian Reward-Certified Outcome Weighted Learning (PROWL) while preserving strict one-sided validity of the reward certificate, i.e., maintaining that the unobserved target reward R* satisfies R* ≥ (R − U)+ almost surely. In particular, construct procedures that mitigate over-correction arising from bounding optimistic error without relying on an exact oracle bias correction, yet still provide guaranteed lower bounds on the true value.

Background

PROWL bounds the latent target value using a one-sided reward certificate, which can lead to conservative estimates in finite samples because it controls optimistic error rather than employing an exact bias correction.

Reducing this conservatism without compromising the one-sided guarantee is crucial for practical deployment, but remains unresolved.

References

Finally, the PROWL framework can be overly conservative in finite samples because it bounds the optimistic error instead of using an exact oracle bias correction. Mitigating this over-correction while maintaining strict one-sided validity remains a crucial open problem.

— PAC-Bayesian Reward-Certified Outcome Weighted Learning  (2604.01946 - Ishikawa et al., 2 Apr 2026) in Section 6 (Discussion)