Integrated vs. sequential approaches for selecting and tuning CMA-ES variants

When faced with a specific optimization problem, deciding which algorithm to apply is always a difficult task. Not only is there a vast variety of algorithms to select from, but these algorithms are often controlled by many hyperparameters, which need to be suitably tuned in order to achieve peak performance. Usually, the problem of selecting and configuring the optimization algorithm is addressed sequentially, by first selecting a suitable algorithm and then tuning it for the application at hand. Integrated approaches, commonly known as Combined Algorithm Selection and Hyperparameter (CASH) solvers, have shown promise in several applications. In this work we compare sequential and integrated approaches for selecting and tuning the best out of the 4,608 variants of the modular Covariance Matrix Adaptation Evolution Strategy (CMA-ES). We show that the ranking of these variants depends to a large extent on the quality of the hyperparameters. Sequential approaches are therefore likely to recommend sub-optimal choices. Integrated approaches, in contrast, manage to provide competitive results at much smaller computational cost. We also highlight important differences in the search behavior of two CASH approaches, which build on racing (irace) and on model-based optimization (MIP-EGO), respectively.