Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space

TL;DR

This paper introduces CMA-ME, a novel quality diversity algorithm that combines CMA-ES and MAP-Elites techniques, achieving superior solution quality and diversity in continuous optimization tasks and strategic game scenarios.

Contribution

The paper presents CMA-ME, a new algorithm that integrates CMA-ES self-adaptation with MAP-Elites, enhancing exploration and solution quality in continuous domains.

Findings

CMA-ME outperforms MAP-Elites in quality solutions.

CMA-ME finds broader diversity of strategies.

CMA-ME more than doubles MAP-Elites' performance.

Abstract

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate a diverse range of solutions, these algorithms require a large number of evaluations for exploration of continuous spaces. 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 self-adaptation techniques of CMA-ES with archiving and mapping techniques for maintaining diversity in QD. Results from experiments based on 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.