利用对称性提升贝叶斯优化效率，无需增加计算开销。
Symmetry-Aware Bayesian Optimization via Max Kernels
- 通过正定投影改进最大核，捕捉函数对称性
- 在合成与真实任务上显著降低累积损失
- 适合具有对称结构的昂贵黑箱优化问题
贝叶斯优化（BO）是优化噪声大、评估成本高的黑箱函数的强大框架。当目标函数在群作用下具有不变性时，利用这些对称性可大幅提升优化效率。尽管最大相似性在其他领域已有应用，但因其非正定性（non-PSD）一直无法用于贝叶斯优化。本文重新审视该方法，提出对最大核进行正定投影。相较于现有不变（及非不变）核，所提方法在合成与真实世界优化基准上均实现显著更低的累积遗憾（regret），且计算复杂度未增加。
原文摘要 · Abstract (English)
Bayesian Optimization (BO) is a powerful framework for optimizing noisy, expensive-to-evaluate black-box functions. When the objective exhibits invariances under a group action, exploiting these symmetries can substantially improve BO efficiency. While using maximum similarity across group orbits has long been considered in other domains, the fact that the max kernel is not positive semidefinite (PSD) has prevented its use in BO. In this work, we revisit this idea by considering a PSD projection of the max kernel. Compared to existing invariant (and non-invariant) kernels, we show it achieves significantly lower regret on both synthetic and real-world BO benchmarks, without increasing computational complexity.
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