Stable Bayesian Optimisation via Direct Stability Quantification
This addresses the need for stable solutions in optimization where input variations cause unacceptable output changes, though it appears incremental as it builds on existing Bayesian optimization methods.
The paper tackles the problem of finding stable maxima for expensive-to-evaluate functions, particularly in physical and industrial processes, by developing an algorithm that uses multiple gradient Gaussian Process models to quantify stability and guide optimization, demonstrating effectiveness on synthetic and real-world problems.
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.