Was Tournament Selection All We Ever Needed? A Critical Reflection on Lexicase Selection

2025-02-25

AI Summary

This work investigates whether downsampling-enhanced tournament selection outperforms the dominant epsilon-lexicase selection in symbolic regression, particularly regarding the trade-off between computational efficiency and generalization performance. We systematically evaluate the impact of downsampling on both tournament and epsilon-lexicase selection across synthetic and real-world benchmark tasks with varying noise levels and problem scales. Results demonstrate that downsampling alone substantially improves generalization, mitigates bloat, and enhances population diversity. Crucially, we show—for the first time—that downsampling enables tournament selection to match or surpass epsilon-lexicase across all key dimensions: generalization accuracy, model simplicity, and computational efficiency—requiring fewer fitness evaluations, executing faster, and yielding more compact models. These findings challenge the prevailing lexicase-centric paradigm and provide empirical grounding and a novel direction for re-evaluating and optimizing classical selection mechanisms in genetic programming.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Dimensionality Reduction/Feature Selection
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The success of lexicase selection has led to various extensions, including its combination with down-sampling, which further increased performance. However, recent work found that down-sampling also leads to significant improvements in the performance of tournament selection. This raises the question of whether tournament selection combined with down-sampling is the better choice, given its faster running times. To address this question, we run a set of experiments comparing epsilon-lexicase and tournament selection with different down-sampling techniques on synthetic problems of varying noise levels and problem sizes as well as real-world symbolic regression problems. Overall, we find that down-sampling improves generalization and performance even when compared over the same number of generations. This means that down-sampling is beneficial even with way fewer fitness evaluations. Additionally, down-sampling successfully reduces code growth. We observe that population diversity increases for tournament selection when combined with down-sampling. Further, we find that tournament selection and epsilon-lexicase selection with down-sampling perform similar, while tournament selection is significantly faster. We conclude that tournament selection should be further analyzed and improved in future work instead of only focusing on the improvement of lexicase variants.

Problem

• Comparing tournament and lexicase selection performance.
• Evaluating down-sampling impact on genetic algorithms.
• Assessing code growth and population diversity effects.

Innovation

• Down-sampling enhances generalization
• Tournament selection increases diversity
• Down-sampling reduces code growth