# Improving Monte Carlo Tree Search for Symbolic Regression

arXiv: https://arxiv.org/abs/2509.15929 · HTML: https://mlsanity.com/paper/2509.15929/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [EPOpt: Learning Robust Neural Network Policies Using Model Ensembles](https://mlsanity.com/paper/1610.01283/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Guiding Deep Molecular Optimization with Genetic Exploration](https://mlsanity.com/paper/2007.04897/) (2020)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data](https://mlsanity.com/paper/2309.13705/) (2023)
- [Monte-Carlo Tree Search by Best Arm Identification](https://mlsanity.com/paper/1706.02986/) (2017)

## Built on by (most cited first, 6 of 6)

- [Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation](https://mlsanity.com/paper/2605.07323/) (2026)
- [When Good Equations Get Bad Scores: Improving Symbolic Regression Through Better Parameter Optimization](https://mlsanity.com/paper/2605.23272/) (2026)
- [EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification](https://mlsanity.com/paper/2606.07915/) (2026)
- [AutoSR: Automatic Symbolic Regression by Searching Research States](https://mlsanity.com/paper/2608.16876/) (2026)
- [SymbolicArena: A Unified Infrastructure for Benchmark Distillation and Dynamic Evaluation in Symbolic Regression](https://mlsanity.com/paper/2609.35113/) (2026)
- [An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation](https://mlsanity.com/paper/2610.12003/) (2026)

## Abstract (arXiv)

Symbolic regression aims to discover concise, interpretable mathematical expressions that satisfy desired objectives, such as fitting data, posing a highly combinatorial optimization problem. While genetic programming has been the dominant approach, recent efforts have explored reinforcement learning methods for improving search efficiency. Monte Carlo Tree Search (MCTS), with its ability to balance exploration and exploitation through guided search, has emerged as a promising technique for symbolic expression discovery. However, its traditional bandit strategies and sequential symbol construction often limit performance. In this work, we propose an improved MCTS framework for symbolic regression that addresses these limitations through two key innovations: (1) an extreme bandit allocation strategy tailored for identifying globally optimal expressions, with finite-time performance guarantees under polynomial reward decay assumptions; and (2) evolution-inspired state-jumping actions such as mutation and crossover, which enable non-local transitions to promising regions of the search space. These state-jumping actions also reshape the reward landscape during the search process, improving both robustness and efficiency. We conduct a thorough numerical study to the impact of these improvements and benchmark our approach against existing symbolic regression methods on a variety of datasets, including both ground-truth and black-box datasets. Our approach achieves competitive performance with state-of-the-art libraries in terms of recovery rate, attains favorable positions on the Pareto frontier of accuracy versus model complexity. Code is available at https://github.com/PKU-CMEGroup/MCTS-4-SR.