aiqbench analysis
This research introduces q-ED-BO, a robust Bayesian optimization framework that replaces standard Gaussian process surrogates with q-exponential distributions to better handle outliers and heavy-tailed noise. By maintaining closed-form tractability for acquisition functions like UCB and EI, the method offers improved resilience in tuning tasks such as beamformer design without sacrificing performance on clean data.
Robust Bayesian Optimization with Q-Exponential Surrogates
arXiv:2609.32775v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2609.32775 [cs.LG]
(or arXiv:2609.32775v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.32775 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 251 words
Related coverage
Online Adaptive Kernel Mixing for Gaussian Process Decision Making
arXiv · Sep 18, 2026
Quantum Gaussian processes for prediction of channel observations
arXiv · Aug 21, 2026
Smart predict-then-robustly-optimize
arXiv · Jul 27, 2026
Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systems
arXiv · Sep 22, 2026