Optimal Decision-Making Based on Prediction Sets
This work addresses a gap in applying prediction sets to real-world decision-making, particularly in safety-critical domains, though it is incremental by building on existing conformal prediction methods.
The paper tackles the problem of using prediction sets optimally for downstream decision-making by proposing a decision-theoretic framework that minimizes expected loss against worst-case distributions, resulting in ROCP, which reduces critical mistakes in tasks like medical diagnosis.
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.