# Sample-efficient Bayesian Optimisation Using Known Invariances

arXiv: https://arxiv.org/abs/2410.16972 · HTML: https://mlsanity.com/paper/2410.16972/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 24 of 24)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Learning with invariances in random features and kernel models](https://mlsanity.com/paper/2102.13219/) (2021)
- [Deep Equals Shallow for ReLU Networks in Kernel Regimes](https://mlsanity.com/paper/2009.14397/) (2020)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [Learning Invariances using the Marginal Likelihood](https://mlsanity.com/paper/1808.05563/) (2018)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Bandit optimisation of functions in the Mat'ern kernel RKHS](https://mlsanity.com/paper/2001.10396/) (2020)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2008.08757/) (2020)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Gaussian Process bandits with adaptive discretization](https://mlsanity.com/paper/1712.01447/) (2017)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Graph Neural Network Bandits](https://mlsanity.com/paper/2207.06456/) (2022)
- [Exploration via Planning for Information about the Optimal Trajectory](https://mlsanity.com/paper/2210.04642/) (2022)
- [Tuning Particle Accelerators with Safety Constraints using Bayesian Optimization](https://mlsanity.com/paper/2203.13968/) (2022)

## Built on by (most cited first, 4 of 4)

- [Symmetry-Aware Bayesian Optimization via Max Kernels](https://mlsanity.com/paper/2509.25051/) (2025)
- [HiBBO: HiPPO-based Space Consistency for High-dimensional Bayesian Optimisation](https://mlsanity.com/paper/2510.08965/) (2025)
- [Reinforcement Learning Using known Invariances](https://mlsanity.com/paper/2511.03473/) (2025)
- [Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications](https://mlsanity.com/paper/2605.02409/) (2026)

## Abstract (arXiv)

Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of transformations. We show that vanilla and constrained BO algorithms are inefficient when optimising such invariant objectives, and provide a method for incorporating group invariances into the kernel of the GP to produce invariance-aware algorithms that achieve significant improvements in sample efficiency. We derive a bound on the maximum information gain of these invariant kernels, and provide novel upper and lower bounds on the number of observations required for invariance-aware BO algorithms to achieve ε-optimality. We demonstrate our method's improved performance on a range of synthetic invariant and quasi-invariant functions. We also apply our method in the case where only some of the invariance is incorporated into the kernel, and find that these kernels achieve similar gains in sample efficiency at significantly reduced computational cost. Finally, we use invariant BO to design a current drive system for a nuclear fusion reactor, finding a high-performance solution where non-invariant methods failed.