Optimal Decision-Making Based on Prediction Sets

TL;DR

This paper develops a decision-theoretic framework for optimally using prediction sets in decision-making, introducing a new method called ROCP that minimizes risk while maintaining coverage, with applications in critical domains.

Contribution

It proposes a novel decision-theoretic approach for optimal decision-making with prediction sets and introduces ROCP, a practical algorithm for risk minimization under coverage constraints.

Findings

ROCP reduces critical mistakes in medical diagnosis.

The framework balances worst-case loss with coverage guarantees.

Empirical results show improved safety in decision-critical tasks.

Abstract

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and safety-critical decision-making tasks demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly.