{"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/a-probabilistic-and-multi-objective-analysis","title":"A probabilistic and multi-objective analysis of lexicase selection and epsilon-lexicase selection","arxiv_id":"1709.05394","date":"2017-09-15","proceeding":null,"authors":["William La Cava","Thomas Helmuth","Lee Spector","Jason H. Moore"],"abstract":"Lexicase selection is a parent selection method that considers training cases\nindividually, rather than in aggregate, when performing parent selection.\nWhereas previous work has demonstrated the ability of lexicase selection to\nsolve difficult problems in program synthesis and symbolic regression, the\ncentral goal of this paper is to develop the theoretical underpinnings that\nexplain its performance. To this end, we derive an analytical formula that\ngives the expected probabilities of selection under lexicase selection, given a\npopulation and its behavior. In addition, we expand upon the relation of\nlexicase selection to many-objective optimization methods to describe the\nbehavior of lexicase selection, which is to select individuals on the\nboundaries of Pareto fronts in high-dimensional space. We show analytically why\nlexicase selection performs more poorly for certain sizes of population and\ntraining cases, and show why it has been shown to perform more poorly in\ncontinuous error spaces. To address this last concern, we propose new variants\nof epsilon-lexicase selection, a method that modifies the pass condition in\nlexicase selection to allow near-elite individuals to pass cases, thereby\nimproving selection performance with continuous errors. We show that\nepsilon-lexicase outperforms several diversity-maintenance strategies on a\nnumber of real-world and synthetic regression problems.","url_abs":"http://arxiv.org/abs/1709.05394v3","url_pdf":"http://arxiv.org/pdf/1709.05394v3.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":"a-probabilistic-and-multi-objective-analysis","repo_url":"https://github.com/lacava/epsilon_lexicase","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"program-synthesis","task_name":"Program Synthesis"},{"task_slug":"symbolic-regression","task_name":"Symbolic Regression"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}