Risk-Controlled Post-Processing of Decision Policies

TL;DR

This paper introduces a risk-controlled post-processing method for decision policies that maximizes agreement with a baseline while satisfying risk constraints, with theoretical guarantees and practical experiments.

Contribution

It develops a threshold-based post-processing algorithm with provable risk control and excess risk bounds, applicable to various decision-making tasks.

Findings

The optimal policy follows the baseline except where it significantly reduces violation risk.

The algorithm achieves an expected excess risk of O(log n/n) under regularity conditions.

Experiments show the method effectively meets risk budgets while maintaining baseline agreement.

Abstract

Predictive models are often deployed through existing decision policies that stakeholders are reluctant to change unless a risk constraint requires intervention. We study risk-controlled post-processing: given a deterministic baseline policy, choose a new policy that maximizes agreement with the baseline subject to a chance constraint on a user-specified loss. At the population level, we show that the optimal policy has a threshold structure: it follows the baseline except on contexts where switching to the oracle fallback policy yields a large reduction in conditional violation risk. At the finite-sample level, given a fitted fallback policy and score, we develop a post-processing algorithm that uses calibration data to select a threshold. Leveraging tools from algorithmic stability and stochastic processes, we show that under regularity conditions, in the i.i.d. setting, the expected excess risk of the post-processed policy is $O(\log n/n)$. In the special case when an exact-safe fallback policy is available, the algorithm achieves precise expected risk control under exchangeability. In this setting, we also give high-probability near-optimality guarantees on the post-processed policy. Experiments on a COVID-19 radiograph diagnosis task, an LLM routing problem, and a synthetic multiclass decision task show that targeted post-processing can meet or nearly meet risk budgets while preserving substantially more agreement with the baseline than score-blind random mixing.