Taylor Polynomial Enhancer using Genetic Programming for Symbolic Regression

Unlike most research of symbolic regression with genetic programming (GP) concerning black-box optimization, this paper focuses on the scenario where the underlying function is available, but due to limited computational resources or product imperfection, the function needs to be approximated with simplicity to fit measured data. Taylor polynomial (TP) is commonly used in such scenario; however, its performance drops drastically away from the expansion point. On the other hand, solely using GP does not utilize the knowledge of the underlying function, even though possibly inaccurate. This paper proposes using GP as a TP enhancer, namely TPE-GP, to combine the advantages from TP and GP. Specifically, TPE-GP utilizes infinite-order operators to compensate the power of TP with finite order. Empirically, on functions that are expressible by TP, TP outperformed both gplearn and TPE-GP as expected, while TPE-GP outperformed gplearn due to the use of TP. On functions that are not expressible by TP but expressible by the function set (FS), TPE-GP was competitive with gplearn while both outperformed TP. Finally, on functions that are not expressible by both TP and FS, TPE-GP outperformed both TP and gplearn, indicating the hybrid did achieve the synergy effect from TP and GP.