AB-GEP: Adversarial bandit gene expression programming for symbolic regression

Abstract

Gene expression programming (GEP) is a commonly used approach for solving symbolic regression (SR) problems. However, GEP often falls into a local optimum. GEP also randomly searches for results and could revisit low value search spaces, which impacts its performance. To overcome the two problems, we propose a new algorithm using an adversarial bandit (AB) technique to enhance GEP and the new algorithm is named AB-GEP. AB-GEP segments the mathematical expression space into many subspaces. It then leverages a new search space selection method, AvgExp3, to enhance the population jump between subspaces. This prevents the algorithm from falling into a local optimum. AvgExp3 dynamically estimates a subspace by the rewards generated in the search space. The dynamical reward estimation makes AB-GEP more adaptive to reward changes and it also provides guidance for AB-GEP to choose a subspace that could contain the correct results. This study proves that AvgExp3 is an unbiased estimation of the average rewards of subspace, and its variance is lower than the standard Exp3 method. The evaluation on two benchmark datasets shows that AB-GEP can maintain better population diversity and obtain better results than three traditional GEPs, GEP, SL-GEP, and SPJ-GEP. AB-GEP ranks top in 50% of the 32 benchmarks, while one of the traditional GEPs only gets no more than 20% of the best results. We release our code at https://github.com/kgae-cup/ab-gep .