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

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arxiv 1912.04871 v4 pith:U6MSTIQI submitted 2019-12-10 cs.LG stat.ML

Brenden K. Petersen , Mikel Landajuela , T. Nathan Mundhenk , Claudio P. Santiago , Soo K. Kim , Joanne T. Kim This is my paper
classification cs.LGstat.ML
keywords symbolicexpressionsregressiondeepmathematicalperformancepolicyrisk-seeking
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 9 Pith papers

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