KL-based Control of the Learning Schedule for Surrogate Black-Box Optimization

TL;DR

This paper introduces a KL-divergence-based method to control the learning schedule of surrogate models in CMA-ES, improving optimization efficiency on complex benchmark problems.

Contribution

It proposes a novel principled approach to determine when to update the surrogate model using KL divergence, enhancing black-box optimization performance.

Findings

Significant performance improvements over state-of-the-art methods.

Effective handling of ill-conditioned benchmark problems.

Outperforms BFGS in various scenarios.

Abstract

This paper investigates the control of an ML component within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) devoted to black-box optimization. The known CMA-ES weakness is its sample complexity, the number of evaluations of the objective function needed to approximate the global optimum. This weakness is commonly addressed through surrogate optimization, learning an estimate of the objective function a.k.a. surrogate model, and replacing most evaluations of the true objective function with the (inexpensive) evaluation of the surrogate model. This paper presents a principled control of the learning schedule (when to relearn the surrogate model), based on the Kullback-Leibler divergence of the current search distribution and the training distribution of the former surrogate model. The experimental validation of the proposed approach shows significant performance gains on a comprehensive set of ill-conditioned benchmark problems, compared to the best state of the art including the quasi-Newton high-precision BFGS method.