Reinforcement Learning for Symbolic Equation Solving
On the map: Deep reinforcement learning methods → Interpretable and logic-guided RL
Abstract (arXiv)
We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods. Builds on 17 of its 25 references that are in the map. First posted on arXiv 31 Aug 2026.
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- 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 309
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- 2017Teacher-Student Curriculum Learningcited by 210
- 2023The Dormant Neuron Phenomenon in Deep Reinforcement Learningcited by 174
- 2025RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimizationcited by 35
- 2021Contrastive Reinforcement Learning of Symbolic Reasoning Domainscited by 17
- 2022Peano: Learning Formal Mathematical Reasoningcited by 15
4 more
- 2023Bad Habits: Policy Confounding and Out-of-Trajectory Generalization in RLcited by 10
- 2026Actor-Curator: Co-adaptive Curriculum Learning via Policy-Improvement Bandits for RL Post-Trainingcited by 8
- 2025Random Scaling of Emergent Capabilitiescited by 7
- 2022LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractionscited by 5
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- 2025Deep Symbolic Optimization: Reinforcement Learning for Symbolic Mathematics
- 2026Learning to Coordinate Symbolic Tools: LLM Agents for Verified Sum-of-Squares Certificates
- 2026VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning