Quality Diversity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are a new class of populationbased 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 betterquality 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 [21] and Hearthstone [20] domains.

Quality diversity (QD) algorithms such as MAP-Elites have emerged as a powerful alternative to traditional single-objective optimization methods. They were initially applied to evolutionary robotics problems such as locomotion and maze navigation, but have yet to see widespread application. We argue that these algorithms are perfectly suited to the rich domain of video games, which contains many relevant problems with a multitude of successful strategies and often also multiple dimensions along which solutions can vary.This paper introduces a novel modification of the MAP-Elites algorithm called MAP-Elites with Sliding Boundaries (MESB) and applies it to the design and rebalancing of Hearthstone, a popular collectible card game chosen for its number of multidimensional behavior features relevant to particular styles of play. To avoid overpopulating cells with conflated behaviors, MESB slides the boundaries of cells based on the distribution of evolved individuals. Experiments in this paper demonstrate the performance of MESB in Hearthstone. Results suggest MESB finds diverse ways of playing the game well along the selected behavioral dimensions. Further analysis of the evolved strategies reveals common patterns that recur across behavioral dimensions and explores how MESB can help rebalance the game.

No abstract