# Stable Bayesian Optimisation via Direct Stability Quantification

## TL;DR

This paper introduces a Bayesian optimization method that quantifies and optimizes for stability in expensive functions, ensuring solutions are robust to input variations in physical and industrial processes.

## Contribution

It develops a novel approach using gradient Gaussian Processes to estimate stability probabilities, guiding optimization toward stable maxima and filtering results for robustness.

## Key findings

- Successfully finds stable maxima in synthetic problems
- Effectively applies to real-world industrial scenarios
- Outperforms traditional optimization methods in stability criteria

## Abstract

In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multiple gradient Gaussian Process models to estimate the probability that worst-case output variation for specified input perturbation exceeded the desired maxima, and these probabilities are then used to (a) guide the optimisation process toward solutions satisfying our stability criteria and (b) post-filter results to find the best stable solution. We exhibit our algorithm on synthetic and real-world problems and demonstrate that it is able to effectively find stable maxima.