Smooth Symbolic Regression: Transformation of Symbolic Regression into a Real-valued Optimization Problem

TL;DR

This paper introduces a method to transform symbolic regression problems into smooth, real-valued optimization problems, facilitating better analysis and potentially improved optimization performance.

Contribution

The authors propose a simple procedure to convert symbolic regression into a smooth real-valued optimization problem, addressing the rugged landscape issue.

Findings

Transformation creates smoother optimization landscapes.

Enables application of standard analysis techniques.

Potentially improves optimization efficiency.

Abstract

The typical methods for symbolic regression produce rather abrupt changes in solution candidates. In this work, we have tried to transform symbolic regression from an optimization problem, with a landscape that is so rugged that typical analysis methods do not produce meaningful results, to one that can be compared to typical and very smooth real-valued problems. While the ruggedness might not interfere with the performance of optimization, it restricts the possibilities of analysis. Here, we have explored different aspects of a transformation and propose a simple procedure to create real-valued optimization problems from symbolic regression problems.