# Informed Down-Sampled Lexicase Selection: Identifying productive training cases for efficient problem solving

arXiv: https://arxiv.org/abs/2301.01488 · HTML: https://mlsanity.com/paper/2301.01488/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2023.

## Built on by (most cited first, 5 of 5)

- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (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)
- [Generational Computation Reduction in Informal Counterexample-Driven Genetic Programming](https://mlsanity.com/paper/2408.12604/) (2024)

## Abstract (arXiv)

Genetic Programming (GP) often uses large training sets and requires all individuals to be evaluated on all training cases during selection. Random down-sampled lexicase selection evaluates individuals on only a random subset of the training cases allowing for more individuals to be explored with the same amount of program executions. However, creating a down-sample randomly might exclude important cases from the current down-sample for a number of generations, while cases that measure the same behavior (synonymous cases) may be overused despite their redundancy. In this work, we introduce Informed Down-Sampled Lexicase Selection. This method leverages population statistics to build down-samples that contain more distinct and therefore informative training cases. Through an empirical investigation across two different GP systems (PushGP and Grammar-Guided GP), we find that informed down-sampling significantly outperforms random down-sampling on a set of contemporary program synthesis benchmark problems. Through an analysis of the created down-samples, we find that important training cases are included in the down-sample consistently across independent evolutionary runs and systems. We hypothesize that this improvement can be attributed to the ability of Informed Down-Sampled Lexicase Selection to maintain more specialist individuals over the course of evolution, while also benefiting from reduced per-evaluation costs.