AI 中文总结
本研究提出ERRLESS方法，将最大熵强化学习与贝叶斯视角结合用于符号回归，在Feynman基准上表现具有竞争力，生成的表达式简短可解释，且后验预测均值的R²优于SMC基线。
AI 中文摘要
符号回归是寻找描述目标变量对一组输入的随机依赖关系的代数表达式的问题。与假设固定模型结构来拟合参数的回归形式不同，符号回归是在表达式空间上的搜索问题，例如使用算子库表示为抽象语法树。符号回归通常用于自然科学中数据有限且有噪声的场景。然而，寻找单个拟合最佳的表达式无法捕捉关于表达式的认知不确定性，这促使人们采用贝叶斯视角，该视角能够进行不确定性量化并指定自然先验以约束搜索空间。在本研究中，我们提出了ERRLESS（用于表达式结构采样的熵正则化强化学习），这是一种使用最大熵强化学习从给定数据的表达式后验分布中采样的可扩展方法。ERRLESS学习一种神经策略，该策略通过逐步构建抽象语法树来顺序构造表达式。收敛时，该策略从后验中采样表达式；测试时，可通过该策略的 rollout（滚动）来采样表达式。我们证明，ERRLESS在Feynman基准上取得了具有竞争力的结果，同时生成了简短且可解释的表达式。此外，我们证明，与SMC基线相比，由ERRLESS近似的后验预测均值达到了较高的决定系数（R²），突出了贝叶斯视角在符号回归中的优势。
英文摘要
Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs. Unlike forms of regression that fit parameters assuming a fixed model structure, symbolic regression is a search problem over the space of expressions, represented, for example, as abstract syntax trees using a library of operators. Symbolic regression is typically used in settings with limited, noisy data in the natural sciences. However, searching for a single best-fitting expression fails to capture the epistemic uncertainty about the expression, which motivates a Bayesian perspective that enables uncertainty quantification and specification of natural priors to constrain the search space. In this work, we propose ERRLESS (Entropy-Regularized Reinforcement Learning for Expression Structure Sampling), a scalable approach for sampling from the posterior distribution over expressions given data using maximum-entropy reinforcement learning. ERRLESS learns a neural policy that constructs expressions sequentially by building up their abstract syntax trees. At convergence, the policy samples expressions from the posterior. At test time, expressions can be sampled by rollouts of this policy. We demonstrate that ERRLESS achieves competitive results on the Feynman benchmark while producing short and interpretable expressions. Additionally, we demonstrate that the mean of the posterior predictive approximated by ERRLESS achieves a high coefficient of determination ($R^2$) compared to an SMC baseline, highlighting the benefits of the Bayesian perspective in symbolic regression.
CommentsUAI 2026. Code available at https://github.com/jaggbow/ERRLESS
