Landscape-Aware Fixed-Budget Performance Regression and Algorithm Selection for Modular CMA-ES Variants
This work addresses the challenge of selecting the best algorithm for optimization problems under time or resource constraints, but it is incremental as it extends existing fixed-target methods to a fixed-budget setting.
The paper tackles the problem of automated algorithm selection for numerical black-box optimization by developing a regression model that predicts algorithm performance within a fixed budget of function evaluations, achieving high-quality predictions using off-the-shelf supervised learning approaches on a portfolio of similar modular CMA-ES variants.
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.