Optimal Decision-Making Based on Prediction Sets

2026-02-01

AI Summary

This work addresses the challenge of optimally leveraging prediction sets for downstream decision-making while guaranteeing a prescribed coverage probability. To this end, the authors propose a decision-theoretic framework that jointly optimizes the construction of prediction sets and the associated decision policy under the worst-case distribution satisfying the coverage constraint. This approach uniquely unifies worst-case loss and out-of-set penalties within a single modeling paradigm. By integrating minimax optimization with risk-sensitive conformal prediction techniques, the method provides rigorous theoretical guarantees while enhancing practical utility. The resulting Risk-Optimized Conformal Prediction (ROCP) algorithm significantly reduces high-cost errors in high-stakes applications such as medical diagnosis, outperforming existing baselines in both safety and performance.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• prediction sets
• optimal decision-making
• minimax risk
• conformal prediction
• worst-case distribution

Innovation

• conformal prediction
• minimax optimization
• risk-optimal decision-making
• prediction sets
• distribution-free coverage