  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.
