想找能处理噪声数据、还能告诉你不确定性有多大的回归方法？ERRLESS用强化学习从后验里采样表达式，Feynman基准上表现不错，表达式还短。
符号回归旨在寻找描述目标变量与输入间随机依赖的代数表达式，不同于固定模型结构的参数拟合，它是在表达式空间中的搜索问题。ERRLESS（熵正则化强化学习用于表达式结构采样）通过最大熵强化学习，学习一个神经网络策略来逐步构建抽象语法树，从而从给定数据的表达式后验分布中采样。在Feynman基准上，ERRLESS取得了有竞争力的结果，同时生成简短且可解释的表达式。与SMC基线相比，ERRLESS近似后验预测均值实现了较高的决定系数（R²），凸显了贝叶斯视角在符号回归中的优势。
Bayesian Symbolic Regression with Entropic Reinforcement Learning
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.