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.

翻译：预测模型通常通过现有的决策策略部署，除非风险约束要求干预，否则利益相关者不愿更改这些策略。我们研究风险控制后处理：给定一个确定性基线策略，选择一个满足用户指定损失的机会约束的新策略，同时最大化与基线策略的一致性。在总体水平上，我们证明最优策略具有阈值结构：除了在切换到预言备用策略能大幅降低条件违规风险的上下文外，该策略遵循基线策略。在有限样本水平上，给定一个拟合的备用策略和分数，我们开发了一种后处理算法，利用校准数据选择阈值。借助算法稳定性和随机过程的工具，我们证明在正则条件下，对于独立同分布设置，后处理策略的期望超额风险为$O(\log n/n)$。在具有精确安全的备用策略这一特殊情况下，该算法在可交换性下实现了精确的期望风险控制。在此设置下，我们还给出了后处理策略的高概率近乎最优性保证。在COVID-19放射影像诊断任务、大语言模型路由问题以及一个合成多类决策任务上的实验表明，有针对性的后处理能够在满足或接近风险预算的同时，相较于对分数无偏见的随机混合，保留与基线策略显著更高的一致性。