{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/covariance-matrix-adaptation-for-the-rapid","title":"Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space","arxiv_id":"1912.02400","date":"2019-12-05","proceeding":null,"authors":["Matthew C. Fontaine","Julian Togelius","Stefanos Nikolaidis","Amy K. Hoover"],"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.","url_abs":"https://arxiv.org/abs/1912.02400v2","url_pdf":"https://arxiv.org/pdf/1912.02400v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/tehqin/EvoStone","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/tehqin/QualDivBenchmark","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/dietmarwo/fast-cma-es","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/icaros-usc/evostone2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/icaros-usc/pyribs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null},{"paper_slug":"covariance-matrix-adaptation-for-the-rapid","repo_url":"https://github.com/schrum2/PyribsForGameGAN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1912.02400","atlas_url":"https://app.syntology.ai/?focus=1912.02400","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1912.02400"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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