Sharpness-Aware Minimization for Evolutionary Feature Construction in Regression

TL;DR

This paper introduces a sharpness-aware minimization technique inspired by PAC-Bayesian theory to improve the robustness and generalization of genetic programming-based feature construction in regression tasks, especially under limited data and noise.

Contribution

It proposes a novel method combining sharpness-aware minimization with genetic programming to reduce overfitting and enhance performance in symbolic regression.

Findings

Outperforms standard GP and complexity measures on 58 datasets

Ensemble GP with sharpness-aware minimization surpasses nine ML algorithms

Effectively mitigates overfitting in noisy or limited data scenarios

Abstract

In recent years, genetic programming (GP)-based evolutionary feature construction has achieved significant success. However, a primary challenge with evolutionary feature construction is its tendency to overfit the training data, resulting in poor generalization on unseen data. In this research, we draw inspiration from PAC-Bayesian theory and propose using sharpness-aware minimization in function space to discover symbolic features that exhibit robust performance within a smooth loss landscape in the semantic space. By optimizing sharpness in conjunction with cross-validation loss, as well as designing a sharpness reduction layer, the proposed method effectively mitigates the overfitting problem of GP, especially when dealing with a limited number of instances or in the presence of label noise. Experimental results on 58 real-world regression datasets show that our approach outperforms standard GP as well as six state-of-the-art complexity measurement methods for GP in controlling overfitting. Furthermore, the ensemble version of GP with sharpness-aware minimization demonstrates superior performance compared to nine fine-tuned machine learning and symbolic regression algorithms, including XGBoost and LightGBM.