Online Adaptive Kernel Mixing for Gaussian Process Decision Making
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Abstract (arXiv)
Gaussian Processes (GPs) are widely used as surrogates for black-box functions in sequential decision-making problems such as Bayesian optimization (BO), level set estimation (LSE), and Bayesian active learning (BAL). GP performance critically depends on kernels, and standard kernels can lead to suboptimal decisions under misspecification. To address this, we introduce HACK GPs (Hedge Adaptive Cumulative Kernels), a method that views kernel selection as an online learning with expert advice problem. HACK treats each candidate kernel as a GP "expert" and updates a distribution over experts online using AdaHedge, based on a loss received as a proxy for their ability to fit the function and align with the task objective. We provide two variants of HACK: (i) Mixture of Gaussians (MoG) and (ii) categorical sampling. We establish general guarantees showing that, under a loss-gap condition, the weight concentrates on the best kernel and the resulting acquisition function is close to that of the best expert. Empirically, we observe robust performance across BO, LSE, and BAL compared to standard kernels such as Squared Exponential and Matern-5/2, as well as simple ensemble baselines.
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References · 12
- 2017Max-value Entropy Search for Efficient Bayesian Optimizationcited by 206
- 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 132
- 2013Structure Discovery in Nonparametric Regression through Compositional Kernel Searchcited by 88
- 2013Follow the Leader If You Can, Hedge If You Mustcited by 70
- 2016Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimationcited by 40
- 2022Bayesian Active Learning with Fully Bayesian Gaussian Processescited by 26
- 2022Surrogate modeling for Bayesian optimization beyond a single Gaussian processcited by 22
- 2025Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMscited by 17
- 2018Robust Super-Level Set Estimation using Gaussian Processescited by 15
- 2024Time-Varying Gaussian Process Bandits with Unknown Priorcited by 11
- 2023Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputscited by 6
- 2025Adaptive Prior Selection in Gaussian Process Bandits with Thompson Samplingcited by 2
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