Symbolic regression is the process of identifying mathematical expressions
that fit observed output from a black-box process. It is a discrete
optimization problem generally believed to be NP-hard. Prior approaches to
solving the problem include neural-guided search (e.g. using reinforcement
learning) and genetic programming. In this work, we introduce a hybrid
neural-guided/genetic programming approach to symbolic regression and other
combinatorial optimization problems. We propose a neural-guided component used
to seed the starting population of a random restart genetic programming
component, gradually learning better starting populations. On a number of
common benchmark tasks to recover underlying expressions from a dataset, our
method recovers 65% more expressions than a recently published top-performing
model using the same experimental setup. We demonstrate that running many
genetic programming generations without interdependence on the neural-guided
component performs better for symbolic regression than alternative formulations
where the two are more strongly coupled. Finally, we introduce a new set of 22
symbolic regression benchmark problems with increased difficulty over existing
benchmarks. Source code is provided at
www.github.com/brendenpetersen/deep-symbolic-optimization.

通过混合神经引导 / 遗传编程方法来优化符号回归问题，表明针对该混合优化方式的神经引导组件可用于改进生产规划初始种群，而分离神经引导和遗传编程组件的生成方式最优，增加了一组 22 个符号回归基准问题。