# Online Adaptive Kernel Mixing for Gaussian Process Decision Making

arXiv: https://arxiv.org/abs/2609.19891 · HTML: https://mlsanity.com/paper/2609.19891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Follow the Leader If You Can, Hedge If You Must](https://mlsanity.com/paper/1301.0534/) (2013)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Bayesian Active Learning with Fully Bayesian Gaussian Processes](https://mlsanity.com/paper/2205.10186/) (2022)
- [Surrogate modeling for Bayesian optimization beyond a single Gaussian process](https://mlsanity.com/paper/2205.14090/) (2022)
- [Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs](https://mlsanity.com/paper/2509.17998/) (2025)
- [Robust Super-Level Set Estimation using Gaussian Processes](https://mlsanity.com/paper/1811.09977/) (2018)
- [Time-Varying Gaussian Process Bandits with Unknown Prior](https://mlsanity.com/paper/2402.01632/) (2024)
- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling](https://mlsanity.com/paper/2502.01226/) (2025)

## 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.