# Epsilon-Lexicase Selection for Regression

## TL;DR

Epsilon-lexicase selection is a novel parent selection method for symbolic regression that improves model accuracy by adaptively redefining test case pass conditions, outperforming traditional techniques with minimal computational cost.

## Contribution

The paper introduces epsilon-lexicase selection, a new variant that enhances regression performance by adaptively adjusting pass criteria for test cases, demonstrating superior results over existing methods.

## Key findings

- Epsilon-lexicase selection produces more accurate models.
- Adaptive epsilon improves selection effectiveness.
- High behavioral diversity observed in lexicase methods.

## Abstract

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 epsilon-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 epsilon and quantify how epsilon affects parent selection and model performance. epsilon-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 epsilon can be adapted automatically for individual test cases based on the population performance distribution. Our experiments show that epsilon-lexicase selection with automatic epsilon 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 epsilon-lexicase selection makes use of more fitness cases when selecting parents than lexicase selection, which helps explain the performance improvement.