Robust Bayesian Optimization via Tempered Posteriors

2026-01-11

AI Summary

This work addresses the issue of overconfident uncertainty quantification in Gaussian process surrogate models within Bayesian optimization, which often leads to suboptimal queries due to underestimated uncertainty in densely sampled local regions. To mitigate this problem caused by local model misspecification, the authors propose a robust Bayesian optimization framework based on a tempered posterior, where a temperature parameter α ∈ (0,1] down-weights the likelihood function. This approach is combined with a generalized improvement-based acquisition function. Furthermore, they introduce a pre-sequential strategy that adaptively selects α online. Theoretical analysis demonstrates that the proposed method achieves lower worst-case cumulative regret compared to standard posterior inference. Empirical results validate its effectiveness in enhancing both calibration and local stability of the surrogate model.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function such as expected improvement (EI). In practice, BO often concentrates evaluations near the current incumbent, causing the surrogate to become overconfident and to understate predictive uncertainty in the region guiding subsequent decisions. We develop a robust GP-based BO via tempered posterior updates, which downweight the likelihood by a power $\alpha \in (0,1]$ to mitigate overconfidence under local misspecification. We establish cumulative regret bounds for tempered BO under a family of generalized improvement rules, including EI, and show that tempering yields strictly sharper worst-case regret guarantees than the standard posterior $(\alpha=1)$, with the most favorable guarantees occurring near the classical EI choice. Motivated by our theoretic findings, we propose a prequential procedure for selecting $\alpha$ online: it decreases $\alpha$ when realized prediction errors exceed model-implied uncertainty and returns $\alpha$ toward one as calibration improves. Empirical results demonstrate that tempering provides a practical yet theoretically grounded tool for stabilizing BO surrogates under localized sampling.

Problem

• Bayesian optimization
• overconfidence
• predictive uncertainty
• Gaussian process
• localized sampling

Innovation

• Tempered Posterior
• Bayesian Optimization
• Gaussian Process
• Overconfidence Mitigation
• Adaptive Calibration