DIRECT Optimisation with Bayesian Insights: Assessing Reliability Under Fixed Computational Budgets

Fu Wang, Zeyu Fu, Xiaowei Huang, Wenjie Ruan

Keywords: DIRECT optimisation, Reliability assessment, Bayesian posterior prediction

TL;DR: Using Bayesian posterior prediction, this paper introduces a method to assess the reliability of DIRECT optimization results under a fixed computational budget, validated through experiments on multi-dimensional test functions

Abstract: We introduce a method for probabilistically evaluating the reliability of Lipschitzian global optimisation under a constrained computational budget, a context frequently encountered in various applications. By interpreting the slope data gathered during the optimisation process as samples from the objective function's derivative, we utilise Bayesian posterior prediction to derive a confidence score for the optimisation outcomes. We validate our approach using numerical experiments on four multi-dimensional test functions, and the results highlight the practicality and efficacy of our approach.

Submission Number: 108