用强化学习引导符号回归,提升复杂函数发现能力。
Beyond Error-Based Optimization: Experience-Driven Symbolic Regression with Goal-Conditioned Reinforcement Learning
- 将符号回归建模为目标条件强化学习,利用历史轨迹指导搜索
- 在相同搜索预算下,恢复率显著高于现有方法,可发现更复杂表达式
- 适合需要高可解释性模型的科研与工程场景
符号回归旨在自动发现紧凑且可解释的数学表达式以建模输入输出变量间的函数关系。现有基于搜索的方法多依赖拟合误差驱动搜索过程,但在庞大的表达式空间中,多个候选表达式可能具有相似误差值但结构差异大,导致搜索方向模糊,难以收敛到真实函数。为此,本文提出一种新框架EGRL-SR(基于经验的目标条件强化学习的符号回归)。不同于传统误差驱动方法,EGRL-SR引入新视角:利用精确的历史轨迹并优化动作价值网络,主动引导搜索过程,实现更稳健的表达式搜索。具体地,将符号回归建模为目标条件强化学习问题,并引入事后经验回放,使动作价值网络能从多样输入-输出对中泛化出常见映射模式。此外,设计全点满足二值奖励函数,促使动作价值网络关注结构模式而非低误差表达式,并提出结构引导的启发式探索策略,增强搜索多样性与空间覆盖。在公开基准上的实验表明,EGRL-SR在恢复率和鲁棒性上持续优于最先进方法,且在相同搜索预算下能恢复更复杂的表达式。消融实验验证了动作价值网络的有效引导作用,奖励函数与探索策略均起关键作用。
原文摘要 · Abstract (English)
Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods typically rely on the fitting error to inform the search process. However, in the vast expression space, numerous candidate expressions may exhibit similar error values while differing substantially in structure, leading to ambiguous search directions and hindering convergence to the underlying true function. To address this challenge, we propose a novel framework named EGRL-SR (Experience-driven Goal-conditioned Reinforcement Learning for Symbolic Regression). In contrast to traditional error-driven approaches, EGRL-SR introduces a new perspective: leveraging precise historical trajectories and optimizing the action-value network to proactively guide the search process, thereby achieving a more robust expression search. Specifically, we formulate symbolic regression as a goal-conditioned reinforcement learning problem and incorporate hindsight experience replay, allowing the action-value network to generalize common mapping patterns from diverse input-output pairs. Moreover, we design an all-point satisfaction binary reward function that encourages the action-value network to focus on structural patterns rather than low-error expressions, and concurrently propose a structure-guided heuristic exploration strategy to enhance search diversity and space coverage. Experiments on public benchmarks show that EGRL-SR consistently outperforms state-of-the-art methods in recovery rate and robustness, and can recover more complex expressions under the same search budget. Ablation results validate that the action-value network effectively guides the search, with both the reward function and the exploration strategy playing critical roles.
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