Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space

Quality Diversity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are a new class of population-based stochastic algorithms designed to generate a diverse collection of quality solutions. Meanwhile, variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are among the best-performing derivative-free optimizers in single-objective continuous domains. This paper proposes a new QD algorithm called Covariance Matrix Adaptation MAP-Elites (CMA-ME). Our new algorithm combines the dynamic self-adaptation techniques of CMA-ES with archiving and mapping techniques for maintaining diversity in QD. Results from experiments with standard continuous optimization benchmarks show that CMA-ME finds better-quality solutions than MAP-Elites; similarly, results on the strategic game Hearthstone show that CMA-ME finds both a higher overall quality and broader diversity of strategies than both CMA-ES and MAP-Elites. Overall, CMA-ME more than doubles the performance of MAP-Elites using standard QD performance metrics. These results suggest that QD algorithms augmented by operators from state-of-the-art optimization algorithms can yield high-performing methods for simultaneously exploring and optimizing continuous search spaces, with significant applications to design, testing, and reinforcement learning among other domains. Code is available for both the continuous optimization benchmark (https://github.com/tehqin/QualDivBenchmark) and Hearthstone (https://github.com/tehqin/EvoStone) domains.