# DALex: Lexicase-like Selection via Diverse Aggregation

arXiv: https://arxiv.org/abs/2401.12424 · HTML: https://mlsanity.com/paper/2401.12424/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [PMLB v1.0: An open source dataset collection for benchmarking machine learning methods](https://mlsanity.com/paper/2012.00058/) (2020)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Lexicase selection in Learning Classifier Systems](https://mlsanity.com/paper/1907.04736/) (2019)
- [Problem-solving benefits of down-sampled lexicase selection](https://mlsanity.com/paper/2106.06085/) (2021)
- [Lexicase Selection at Scale](https://mlsanity.com/paper/2208.10719/) (2022)
- [Informed Down-Sampled Lexicase Selection: Identifying productive training cases for efficient problem solving](https://mlsanity.com/paper/2301.01488/) (2023)
- [Lexicase Selection of Specialists](https://mlsanity.com/paper/1905.09372/) (2019)
- [Code Building Genetic Programming](https://mlsanity.com/paper/2008.03649/) (2020)
- [Batch Tournament Selection for Genetic Programming](https://mlsanity.com/paper/1904.08658/) (2019)
- [Calculating lexicase selection probabilities is NP-Hard](https://mlsanity.com/paper/2301.06724/) (2023)
- [Probabilistic Lexicase Selection](https://mlsanity.com/paper/2305.11681/) (2023)
- [Particularity](https://mlsanity.com/paper/2306.06812/) (2023)
- [Population Diversity Leads to Short Running Times of Lexicase Selection](https://mlsanity.com/paper/2204.06461/) (2022)
- [Optimizing Neural Networks with Gradient Lexicase Selection](https://mlsanity.com/paper/2312.12606/) (2023)

## Built on by (most cited first, 3 of 3)

- [Pareto-Optimal Learning from Preferences with Hidden Context](https://mlsanity.com/paper/2406.15599/) (2024)
- [Vector Policy Optimization: Training for Diversity Improves Test-Time Search](https://mlsanity.com/paper/2605.22817/) (2026)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)

## Abstract (arXiv)

Lexicase selection has been shown to provide advantages over other selection algorithms in several areas of evolutionary computation and machine learning. In its standard form, lexicase selection filters a population or other collection based on randomly ordered training cases that are considered one at a time. This iterated filtering process can be time-consuming, particularly in settings with large numbers of training cases. In this paper, we propose a new method that is nearly equivalent to lexicase selection in terms of the individuals that it selects, but which does so significantly more quickly. The new method, called DALex (for Diversely Aggregated Lexicase), selects the best individual with respect to a weighted sum of training case errors, where the weights are randomly sampled. This allows us to formulate the core computation required for selection as matrix multiplication instead of recursive loops of comparisons, which in turn allows us to take advantage of optimized and parallel algorithms designed for matrix multiplication for speedup. Furthermore, we show that we can interpolate between the behavior of lexicase selection and its "relaxed" variants, such as epsilon or batch lexicase selection, by adjusting a single hyperparameter, named "particularity pressure," which represents the importance granted to each individual training case. Results on program synthesis, deep learning, symbolic regression, and learning classifier systems demonstrate that DALex achieves significant speedups over lexicase selection and its relaxed variants while maintaining almost identical problem-solving performance. Under a fixed computational budget, these savings free up resources that can be directed towards increasing population size or the number of generations, enabling the potential for solving more difficult problems.