Landscape-Aware Fixed-Budget Performance Regression and Algorithm Selection for Modular CMA-ES Variants

TL;DR

This paper develops a landscape-aware performance regression method for fixed-budget algorithm selection in black-box optimization, demonstrating high prediction quality using combined models on CMA-ES variants.

Contribution

It introduces a novel fixed-budget performance regression approach based on exploratory landscape analysis and combined models for algorithm selection.

Findings

High-quality performance predictions achieved with simple supervised models.

Effective combination of two regression models improves prediction accuracy.

Demonstrated approach on modular CMA-ES variants with challenging problem instances.

Abstract

Automated algorithm selection promises to support the user in the decisive task of selecting a most suitable algorithm for a given problem. A common component of these machine-trained techniques are regression models which predict the performance of a given algorithm on a previously unseen problem instance. In the context of numerical black-box optimization, such regression models typically build on exploratory landscape analysis (ELA), which quantifies several characteristics of the problem. These measures can be used to train a supervised performance regression model. First steps towards ELA-based performance regression have been made in the context of a fixed-target setting. In many applications, however, the user needs to select an algorithm that performs best within a given budget of function evaluations. Adopting this fixed-budget setting, we demonstrate that it is possible to achieve high-quality performance predictions with off-the-shelf supervised learning approaches, by suitably combining two differently trained regression models. We test this approach on a very challenging problem: algorithm selection on a portfolio of very similar algorithms, which we choose from the family of modular CMA-ES algorithms.