Risk-Controlled Post-Processing of Decision Policies
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914539810848768 |
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| author | Joshi, Sunay Wang, Tao Hassani, Hamed Dobriban, Edgar |
| author_facet | Joshi, Sunay Wang, Tao Hassani, Hamed Dobriban, Edgar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Risk-Controlled Post-Processing of Decision Policies Joshi, Sunay Wang, Tao Hassani, Hamed Dobriban, Edgar Machine Learning Statistics Theory 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. |
| title | Risk-Controlled Post-Processing of Decision Policies |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2605.06479 |