Benchmarking symbolic regression constant optimization schemes

TL;DR

This paper evaluates eight constant optimization methods in symbolic regression using genetic programming across ten benchmarks, introduces Tree Edit Distance as a new metric, and analyzes their performance and biases.

Contribution

It provides a comparative analysis of constant optimization schemes, introduces Tree Edit Distance for symbolic accuracy, and discusses metric biases in symbolic regression.

Findings

Different methods excel in different scenarios.

No single method is best for all problems.

Common metrics may bias model evaluation.

Abstract

Symbolic regression is a machine learning technique, and it has seen many advancements in recent years, especially in genetic programming approaches (GPSR). Furthermore, it has been known for many years that constant optimization of parameters, during the evolutionary search, greatly increases GPSR performance However, different authors approach such tasks differently and no consensus exists regarding which methods perform best. In this work, we evaluate eight different parameter optimization methods, applied during evolutionary search, over ten known benchmark problems, in two different scenarios. We also propose using an under-explored metric called Tree Edit Distance (TED), aiming to identify symbolic accuracy. In conjunction with classical error measures, we develop a combined analysis of model performance in symbolic regression. We then show that different constant optimization methods perform better in certain scenarios and that there is no overall best choice for every problem. Finally, we discuss how common metric decisions may be biased and appear to generate better models in comparison.