Interval Arithmetic and Interval-Aware Operators for Genetic Programming

TL;DR

This paper explores the use of interval arithmetic and interval-aware operators in genetic programming for symbolic regression, aiming to improve model validity and generalization without relying on protected operators.

Contribution

It introduces safe interval-aware operators that reduce invalid solutions and enhance the search for models with better generalization in genetic programming.

Findings

Interval arithmetic alone does not prevent invalid solutions.

Interval-aware operators significantly reduce invalid solutions.

Models using interval-aware operators generalize better to unseen data.

Abstract

Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regression require the use of protected operators, which can lead to perverse model characteristics and poor generalisation. In this paper, we revisit interval arithmetic as one possible solution to allow genetic programming to perform regression using unprotected operators. Using standard benchmarks, we show that using interval arithmetic within model evaluation does not prevent invalid solutions from entering the population, meaning that search performance remains compromised. We extend the basic interval arithmetic concept with `safe' search operators that integrate interval information into their process, thereby greatly reducing the number of invalid solutions produced during search. The resulting algorithms are able to more effectively identify good models that generalise well to unseen data. We conclude with an analysis of the sensitivity of interval arithmetic-based operators with respect to the accuracy of the supplied input feature intervals.