This paper proposes a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Despite the success of the state-of-the-art method, DSR, it is built on recurrent neural networks, purely guided by data fitness, and potentially meet tail barriers, which can zero out the policy gradient and cause inefficient model updates. To overcome these limitations, we use transformers in conjunction with breadth-first-search to improve the learning performance. We use Bayesian information criterion (BIC) as the reward function to explicitly account for the expression complexity and optimize the trade-off between interpretability and data fitness. We propose a modified risk-seeking policy that not only ensures the unbiasness of the gradient, but also removes the tail barriers, thus ensuring effective updates from top performers. Through a series of benchmarks and systematic experiments, we demonstrate the advantages of our approach.

本文提出了一种新颖的深度符号回归方法，以增强数据驱动的数学表达式发现的鲁棒性和解释性。通过使用transformer与广度优先搜索相结合来改善学习性能，并使用贝叶斯信息准则（BIC）作为奖励函数来明确考虑表达式复杂性并优化解释性和数据适应性之间的权衡。通过一系列基准测试和系统性实验，我们展示了我们方法的优势。

具备复杂性意识的深度符号回归与稳健风险寻求策略梯度