高斯过程决策中的在线自适应核混合
Online Adaptive Kernel Mixing for Gaussian Process Decision Making
- International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）
- Arizona State University（亚利桑那州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出HACK GPs方法，将核选择视为在线专家学习问题，通过AdaHedge更新核权重，在贝叶斯优化、水平集估计和主动学习中实现稳健性能。
AI中文摘要：
高斯过程（GPs）在贝叶斯优化（BO）、水平集估计（LSE）和贝叶斯主动学习（BAL）等序贯决策问题中广泛用作黑箱函数的代理模型。GP的性能关键取决于核函数，而标准核函数在设定错误（misspecification）下可能导致次优决策。为解决此问题，我们提出HACK GPs（Hedge自适应累积核），一种将核选择视为在线学习与专家建议问题的方法。HACK将每个候选核视为一个GP“专家”，并使用AdaHedge在线更新专家上的分布，其依据是作为代理的损失，该损失反映专家拟合函数及与任务目标对齐的能力。我们提供HACK的两种变体：（i）高斯混合（MoG）和（ii）分类采样。我们建立了通用保证，表明在损失间隙条件下，权重集中于最佳核，且由此产生的采集函数接近最佳专家的采集函数。实验上，我们观察到在BO、LSE和BAL中，与标准核（如平方指数核和Matern-5/2核）以及简单集成基线相比，HACK表现出稳健的性能。
英文摘要：
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.
