Parallel black-box optimization of expensive high-dimensional multimodal functions via magnitude

TL;DR

This paper introduces EXPLO2, a new black-box optimization algorithm designed for high-dimensional, multimodal, and expensive functions, leveraging the theory of magnitude to improve optimization performance.

Contribution

The paper presents EXPLO2, a novel optimization algorithm that advances the state of the art for high-dimensional, multimodal, derivative-free functions using the theory of magnitude.

Findings

EXPLO2 outperforms existing methods on benchmark problems.

It effectively handles functions with dimensions greater than 40.

The approach is suitable for hyperparameter tuning and simulation-based optimization.

Abstract

Building on the recently developed theory of magnitude, we introduce the optimization algorithm EXPLO2 and carefully benchmark it. EXPLO2 advances the state of the art for optimizing high-dimensional ($D \gtrapprox 40$) multimodal functions that are expensive to compute and for which derivatives are not available, such as arise in hyperparameter optimization or via simulations.