# Symmetry-Aware Bayesian Optimization via Max Kernels

arXiv: https://arxiv.org/abs/2509.25051 · HTML: https://mlsanity.com/paper/2509.25051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [On the Sublinear Regret of GP-UCB](https://mlsanity.com/paper/2307.07539/) (2023)
- [Bayesian Optimization using Pseudo-Points](https://mlsanity.com/paper/1910.05484/) (2019)
- [This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization](https://mlsanity.com/paper/2405.14540/) (2024)
- [Sample-efficient Bayesian Optimisation Using Known Invariances](https://mlsanity.com/paper/2410.16972/) (2024)
- [INSPIRE: Distributed Bayesian Optimization for ImproviNg SPatIal REuse in Dense WLANs](https://mlsanity.com/paper/2204.10184/) (2022)

## Abstract (arXiv)

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.