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DALex: Lexicase-Like Selection via Diverse Aggregation

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Genetic Programming (EuroGP 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14631))

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Abstract

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, including many symbolic regression and deep learning applications. 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 in significantly less time. The new method, called DALex (for Diversely Aggregated Lexicase selection), selects the best individual with respect to a randomly weighted sum of training case errors. 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 and 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.

Supported by Amherst College and members of the PUSH lab.

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Notes

  1. 1.

    https://arxiv.org/abs/2401.12424.

  2. 2.

    Fixed a bug in the downsampling implementation in the released version of [8].

  3. 3.

    Due to specific quirks of the code-building system, it is very difficult for CBGP to generalize successfully on Compare String Lengths.

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Acknowledgements

This work was performed in part using high-performance computing equipment at Amherst College obtained under National Science Foundation Grant No. 2117377. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would like to thank Ryan Boldi, Bill Tozier, Tom Helmuth, Edward Pantridge and other members of the PUSH lab for their insightful comments and suggestions.

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Authors and Affiliations

  1. Amherst College, Amherst, MA, 01002, USA

    Andrew Ni & Lee Spector

  2. University of Massachusetts Amherst, Amherst, MA, 01003, USA

    Li Ding & Lee Spector

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  1. Andrew Ni
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  2. Li Ding
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Correspondence to Andrew Ni .

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  1. University of Torino, Grugliasco, Italy

    Mario Giacobini

  2. Victoria University of Wellington, Wellington, New Zealand

    Bing Xue

  3. University of Trieste, Trieste, Italy

    Luca Manzoni

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Ni, A., Ding, L., Spector, L. (2024). DALex: Lexicase-Like Selection via Diverse Aggregation. In: Giacobini, M., Xue, B., Manzoni, L. (eds) Genetic Programming. EuroGP 2024. Lecture Notes in Computer Science, vol 14631. Springer, Cham. https://doi.org/10.1007/978-3-031-56957-9_6

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