Robust Bayesian Optimization with Q-Exponential Surrogates

2026-09-26

AI Summary

This study addresses the high sensitivity of Gaussian process (GP) surrogate models to outliers and heavy-tailed noise in Bayesian optimization. To this end, it proposes the q-ED-BO framework, which leverages the q-exponential distribution to construct a robust surrogate model. By tuning tail behavior through a shape parameter, the approach enhances outlier tolerance while preserving the closed-form analytical advantages of GPs. Furthermore, closed-form q-UCB and generalized q-EI acquisition functions with sublinear regret bounds are derived. Experimental evaluations on beamforming and adaptive filtering tasks under impulsive noise demonstrate that the proposed method achieves an approximate 0.7 dB improvement in signal-to-interference-plus-noise ratio and a 1.1–1.2 dB reduction in misalignment, significantly outperforming existing baselines.

Abstract

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.

Problem

• Bayesian Optimization
• Robustness
• Outliers
• Heavy-tailed Noise
• Gaussian Process

Innovation

• Bayesian Optimization
• q-Exponential Distribution
• Robust Surrogate Model
• Acquisition Function
• Heavy-tailed Noise