# Safe Bayesian Optimization with Counterfactual Policies

arXiv: https://arxiv.org/abs/2607.05620 · HTML: https://mlsanity.com/paper/2607.05620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Bandits with concave rewards and convex knapsacks](https://mlsanity.com/paper/1402.5758/) (2014)
- [Linear Contextual Bandits with Knapsacks](https://mlsanity.com/paper/1507.06738/) (2015)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Bandits](https://mlsanity.com/paper/1504.06937/) (2015)
- [Bayesian Optimization with Formal Safety Guarantees via Online Conformal Prediction](https://mlsanity.com/paper/2306.17815/) (2023)
- [Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence](https://mlsanity.com/paper/2312.03212/) (2023)

## Abstract (arXiv)

In many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizes an objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.