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

We introduce a method for probabilistically evaluating the reliability of direct 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 validated our approach using numerical experiments on four multi-dimensional test functions, and the results highlight the practicality and efficacy of our approach.