论文标题
使用语法指导的符号回归来实现领域知识包容的强化学习方法
A Reinforcement Learning Approach to Domain-Knowledge Inclusion Using Grammar Guided Symbolic Regression
论文作者
论文摘要
近年来，符号回归引起了广泛的兴趣，以提供对潜在大数据关系的可解释符号表示。符号回归方法最初循环到遗传算法上，现在包括各种基于深度学习的替代方案。但是，这些方法仍然不能很好地推广到现实世界数据，主要是因为它们几乎不包括域知识，也不考虑已知方程和单位等变量之间的物理关系。关于这些问题，我们提出了一种基于增强的语法引导符号回归（RBG2-SR）方法，该方法将用无上下文的语法作为增强动作空间来约束代表空间，并以域知识约束域知识。我们详细介绍了对问题的部分观察到的马尔可夫决策过程（POMDP）建模，并根据最先进的方法为我们的方法进行基准测试。我们还分析了POMDP状态定义，并提出了一个物理方程搜索用例，我们将我们的方法比较了基于语法和基于语法的符号回归方法。实验结果表明，我们的方法与基准上的其他最先进方法具有竞争力，并提供了最佳的错误复杂性权衡取舍，这突出了在现实世界中使用基于语法的方法的兴趣。
In recent years, symbolic regression has been of wide interest to provide an interpretable symbolic representation of potentially large data relationships. Initially circled to genetic algorithms, symbolic regression methods now include a variety of Deep Learning based alternatives. However, these methods still do not generalize well to real-world data, mainly because they hardly include domain knowledge nor consider physical relationships between variables such as known equations and units. Regarding these issues, we propose a Reinforcement-Based Grammar-Guided Symbolic Regression (RBG2-SR) method that constrains the representational space with domain-knowledge using context-free grammar as reinforcement action space. We detail a Partially-Observable Markov Decision Process (POMDP) modeling of the problem and benchmark our approach against state-of-the-art methods. We also analyze the POMDP state definition and propose a physical equation search use case on which we compare our approach to grammar-based and non-grammarbased symbolic regression methods. The experiment results show that our method is competitive against other state-of-the-art methods on the benchmarks and offers the best error-complexity trade-off, highlighting the interest of using a grammar-based method in a real-world scenario.
