Bayesian Optimization for Quality Diversity Search With Coupled Descriptor Functions

Paul Kent, Adam Gaier, Jean-Baptiste Mouret, Juergen Branke

Abstract: Quality diversity (QD) algorithms, such as the multidimensional archive of phenotypic elites (MAP-Elites), are a class of optimization techniques that attempt to find many high-performing points that all behave differently according to a user-defined behavioral metric. In this article we propose the Bayesian optimization of elites (BOP-Elites) algorithm. Designed for problems with expensive fitness functions and coupled behavior descriptors, it is able to return a QD solution-set with excellent performance already after a relatively small number of samples. BOP-Elites models both fitness and behavioral descriptors with Gaussian Process surrogate models and uses Bayesian optimization strategies for choosing points to evaluate in order to solve the quality-diversity problem. In addition, BOP-Elites produces high-quality surrogate models which can be used after convergence to predict solutions with any behavior in a continuous range. An empirical comparison shows that BOP-Elites significantly outperforms other state-of-the-art algorithms without the need for problem-specific parameter tuning.