Epsilon-Lexicase Selection for Regression

Lexicase selection is a parent selection method that considers test cases separately, rather than in aggregate, when performing parent selection. It performs well in discrete error spaces but not on the continuous-valued problems that compose most system identification tasks. In this paper, we develop a new form of lexicase selection for symbolic regression, named ε-lexicase selection, that redefines the pass condition for individuals on each test case in a more effective way. We run a series of experiments on real-world and synthetic problems with several treatments of ε and quantify how ε affects parent selection and model performance. ε-lexicase selection is shown to be effective for regression, producing better fit models compared to other techniques such as tournament selection and age-fitness Pareto optimization. We demonstrate that ε can be adapted automatically for individual test cases based on the population performance distribution. Our experiments show that ε-lexicase selection with automatic ε produces the most accurate models across tested problems with negligible computational overhead. We show that behavioral diversity is exceptionally high in lexicase selection treatments, and that ε-lexicase selection makes use of more fitness cases when selecting parents than lexicase selection, which helps explain the performance improvement.