# Epsilon-Lexicase Selection for Regression

arXiv: https://arxiv.org/abs/1905.13266 · HTML: https://mlsanity.com/paper/1905.13266/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 30 of 31)

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- [Lexicase Selection at Scale](https://mlsanity.com/paper/2208.10719/) (2022)
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- [Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback](https://mlsanity.com/paper/2505.15572/) (2025)
- [Probabilistic Lexicase Selection](https://mlsanity.com/paper/2305.11681/) (2023)
- [Particularity](https://mlsanity.com/paper/2306.06812/) (2023)
- [DALex: Lexicase-like Selection via Diverse Aggregation](https://mlsanity.com/paper/2401.12424/) (2024)
- [Optimizing Neural Networks with Gradient Lexicase Selection](https://mlsanity.com/paper/2312.12606/) (2023)
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- [Towards symbolic regression for interpretable clinical decision scores](https://mlsanity.com/paper/2512.07961/) (2025)
- [FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression](https://mlsanity.com/paper/2605.12704/) (2026)
- [Zoetrope Genetic Programming for Regression](https://mlsanity.com/paper/2102.13388/) (2021)
- [EBIC.JL -- an Efficient Implementation of Evolutionary Biclustering Algorithm in Julia](https://mlsanity.com/paper/2105.01196/) (2021)
- [Faster Convergence with Lexicase Selection in Tree-based Automated Machine Learning](https://mlsanity.com/paper/2302.00731/) (2023)
- [Learning Difference Equations with Structured Grammatical Evolution for Postprandial Glycaemia Prediction](https://mlsanity.com/paper/2307.01238/) (2023)
- [UniSymNet: A Unified Symbolic Network Guided by Transformer](https://mlsanity.com/paper/2505.06091/) (2025)
- [Decoupling Representation and Learning in Genetic Programming: the LaSER Approach](https://mlsanity.com/paper/2505.17309/) (2025)
- [Auditable Unit-Aware Thresholds in Symbolic Regression via Logistic-Gated Operators](https://mlsanity.com/paper/2510.05178/) (2025)

## Abstract (arXiv)

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.