Interactive symbolic regression with co-design mechanism through offline reinforcement learning

Symbolic Regression holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for previous online search methods and pre-trained transformer models, which mostly do not consider the integration of domain experts' prior knowledge. To address these challenges, we propose the Symbolic Q-network, an advanced interactive framework for large-scale symbolic regression. Unlike previous transformer-based SR approaches, Symbolic Q-network leverages reinforcement learning without relying on a transformer-based decoder. Furthermore, we propose a co-design mechanism, where the Symbolic Q-network facilitates effective interaction with domain experts at any stage of the equation discovery process. Our extensive experiments demonstrate Sym-Q performs comparably to existing pretrained models across multiple benchmarks. Furthermore, our experiments on real-world cases demonstrate that the interactive co-design mechanism significantly enhances Symbolic Q-network's performance, achieving greater performance gains than standard autoregressive models.