# Robust Bayesian Optimization via Localized Online Conformal Prediction

arXiv: https://arxiv.org/abs/2411.17387 · HTML: https://mlsanity.com/paper/2411.17387/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 30 of 31)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [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)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Meta-Learning Acquisition Functions for Transfer Learning in Bayesian Optimization](https://mlsanity.com/paper/1904.02642/) (2019)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)
- [Meta-Learning Priors for Safe Bayesian Optimization](https://mlsanity.com/paper/2210.00762/) (2022)
- [Uncertainty quantification using martingales for misspecified Gaussian processes](https://mlsanity.com/paper/2006.07368/) (2020)
- [Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation](https://mlsanity.com/paper/1910.07779/) (2019)
- [Active emulation of computer codes with Gaussian processes -- Application to remote sensing](https://mlsanity.com/paper/1912.06552/) (2019)
- [Online Calibrated and Conformal Prediction Improves Bayesian Optimization](https://mlsanity.com/paper/2112.04620/) (2021)
- [Bayesian and Multi-Armed Contextual Meta-Optimization for Efficient Wireless Radio Resource Management](https://mlsanity.com/paper/2301.06510/) (2023)
- [Adaptive quadrature schemes for Bayesian inference via active learning](https://mlsanity.com/paper/2006.00535/) (2020)
- [Heteroscedastic Bayesian Optimisation for Stochastic Model Predictive Control](https://mlsanity.com/paper/2010.00202/) (2020)
- [Tight Regret Bounds for Noisy Optimization of a Brownian Motion](https://mlsanity.com/paper/2001.09327/) (2020)
- [Multi-Fidelity Bayesian Optimization With Across-Task Transferable Max-Value Entropy Search](https://mlsanity.com/paper/2403.09570/) (2024)
- [From Conformal Predictions to Confidence Regions](https://mlsanity.com/paper/2405.18601/) (2024)
- [Bayesian Active Meta-Learning for Black-Box Optimization](https://mlsanity.com/paper/2110.09943/) (2021)

## Built on by (most cited first, 1 of 1)

- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.