# Robust Bayesian Optimization with Q-Exponential Surrogates

arXiv: https://arxiv.org/abs/2609.32775 · HTML: https://mlsanity.com/paper/2609.32775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Bayesian Optimization under Heavy-tailed Payoffs](https://mlsanity.com/paper/1909.07040/) (2019)
- [Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs](https://mlsanity.com/paper/2509.17998/) (2025)
- [Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series](https://mlsanity.com/paper/1904.09559/) (2019)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Robust Bayesian Optimization via Tempered Posteriors](https://mlsanity.com/paper/2601.07094/) (2026)
- [Sparsity-Aware Distributed Learning for Gaussian Processes with Linear Multiple Kernel](https://mlsanity.com/paper/2309.08201/) (2023)

## Abstract (arXiv)

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box objectives, but standard BO methods often use Gaussian process (GP) surrogates whose Gaussian assumption is sensitive to outliers and heavy-tailed noise. We introduce q-ED-BO, a robust BO method whose surrogate follows a univariate q-exponential (q-ED) distribution, preserving GP-BO's closed-form posterior mean and variance while a shape parameter q controls the tail behavior, recovering the GP at q = 2 and growing heavier-tailed with wider confidence bounds as q decreases. This tractability yields a closed-form q-upper confidence bound (q-UCB) with sublinear regret, and an exact closed-form q-expected improvement (q-EI) that generalizes EI to the heavy-tailed predictive, recovering classical EI at q = 2. Experiments on beamformer and adaptive filter tuning with impulsive outliers show that q-ED-BO matches or exceeds existing baselines on clean data, and under corruption, improves the strongest baseline by approximately 0.7 dB in output SINR and 1.1 to 1.2 dB in misalignment reduction.