Progressive Subexpression Reuse in Symbolic Regression: Insights from RL-based Search and a Genetic Programming Realization

Wu, Xiangdong; Wu, Wenjun; Chen, Bingrun; Wang, Junle; Fan, Zhaoxin; Zhou, Haoyi; Zhang, Pengju; Shi, Rongye

doi:10.24963/ijcai.2026/564

Progressive Subexpression Reuse in Symbolic Regression: Insights from RL-based Search and a Genetic Programming Realization

Xiangdong Wu, Wenjun Wu, Bingrun Chen, Junle Wang, Zhaoxin Fan, Haoyi Zhou, Pengju Zhang, Rongye Shi

Download BibTeX Cite

Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 5066-5073.

https://doi.org/10.24963/ijcai.2026/564

Keywords

Machine Learning: Regression
Machine Learning: Reinforcement learning
Search: Evolutionary computation

Abstract

Symbolic regression (SR) aims to recover compact and interpretable mathematical expressions from data.

Genetic programming (GP) directly searches over symbolic structures, but its population dynamics can make it difficult to reliably preserve and accumulate useful subexpressions.

In contrast, reinforcement learning (RL)-based SR has shown strong empirical performance, suggesting that learned sampling dynamics may capture useful regularities in symbolic search.

Motivated by this contrast, we analyze expressions sampled during RL training and identify a recurring pattern, termed progressive subexpression reuse, where useful simple subexpressions emerge early, become increasingly frequent, and support the formation of more complex structures.

Based on this observation, we propose Reinforcement Genetic Programming (RGP), a purely GP-based and non-RL framework that explicitly realizes a stage-wise retention--reintroduction loop through a dynamically maintained subexpression pool and pool-guided population initialization.

Experiments on standard SR benchmarks show that RGP matches or outperforms strong baselines without RL policy training, suggesting that progressive subexpression reuse is an effective mechanism for SR search. We release our code at https://github.com/wuxiangdong586-max/RGP.

Xiangdong Wu, Wenjun Wu, Bingrun Chen, Junle Wang, Zhaoxin Fan, Haoyi Zhou, Pengju Zhang, and Rongye Shi. 2026. Progressive Subexpression Reuse in Symbolic Regression: Insights from RL-based Search and a Genetic Programming Realization. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 5066–5073. https://doi.org/10.24963/ijcai.2026/564

@inproceedings{ijcai2026p564,
  title     = {Progressive Subexpression Reuse in Symbolic Regression: Insights from RL-based Search and a Genetic Programming Realization},
  author    = {Wu, Xiangdong and Wu, Wenjun and Chen, Bingrun and Wang, Junle and Fan, Zhaoxin and Zhou, Haoyi and Zhang, Pengju and Shi, Rongye},
  booktitle = {Proceedings of the Thirty-Fifth International Joint Conference on
               Artificial Intelligence, {IJCAI-26}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Diego Calvanese},
  pages     = {5066--5073},
  year      = {2026},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2026/564},
  url       = {https://doi.org/10.24963/ijcai.2026/564},
}

TY  - CPAPER
TI  - Progressive Subexpression Reuse in Symbolic Regression: Insights from RL-based Search and a Genetic Programming Realization
AU  - Wu, Xiangdong
AU  - Wu, Wenjun
AU  - Chen, Bingrun
AU  - Wang, Junle
AU  - Fan, Zhaoxin
AU  - Zhou, Haoyi
AU  - Zhang, Pengju
AU  - Shi, Rongye
T2  - Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2026
SP  - 5066
EP  - 5073
DO  - 10.24963/ijcai.2026/564
UR  - https://doi.org/10.24963/ijcai.2026/564
ER  -