## Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Sep 28, 2020 (edited Apr 09, 2021)ICLR 2021 OralReaders: Everyone
• Keywords: symbolic regression, reinforcement learning, automated machine learning
• Abstract: Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that leverages deep learning for symbolic regression via a simple idea: use a large model to search the space of small models. Specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions and employ a novel risk-seeking policy gradient to train the network to generate better-fitting expressions. Our algorithm outperforms several baseline methods (including Eureqa, the gold standard for symbolic regression) in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.
• One-sentence Summary: A deep learning approach to symbolic regression, in which an autoregressive RNN emits a distribution over expressions that is optimized using a risk-seeking policy gradient.
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