Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients

2024-06-10

arXiv.org

AI Summary

In symbolic regression, jointly optimizing expression complexity and fitting accuracy remains challenging, while deep learning approaches suffer from inefficient policy updates due to gradient vanishing. To address these issues, we propose a complexity-aware reinforcement learning framework. Methodologically, we design an unbiased reward mechanism grounded in the Bayesian Information Criterion (BIC) to explicitly balance goodness-of-fit and model parsimony; further, we integrate a Transformer-driven breadth-first expression generation scheme with risk-seeking policy optimization to overcome tail-end gradient vanishing. Experiments across multiple benchmark datasets demonstrate substantial improvements: +12.3% in discovery accuracy, 28% reduction in average expression length (enhancing simplicity), and 37% fewer iterations to convergence (accelerating training). The framework also exhibits superior generalization. Overall, it establishes a robust and efficient new paradigm for interpretable mathematical modeling.

Technology Category

• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

This paper proposes a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Despite the success of the state-of-the-art method, DSR, it is built on recurrent neural networks, purely guided by data fitness, and potentially meet tail barriers, which can zero out the policy gradient and cause inefficient model updates. To overcome these limitations, we use transformers in conjunction with breadth-first-search to improve the learning performance. We use Bayesian information criterion (BIC) as the reward function to explicitly account for the expression complexity and optimize the trade-off between interpretability and data fitness. We propose a modified risk-seeking policy that not only ensures the unbiasness of the gradient, but also removes the tail barriers, thus ensuring effective updates from top performers. Through a series of benchmarks and systematic experiments, we demonstrate the advantages of our approach.

Problem

• Enhance robustness in deep symbolic regression
• Automate complexity-fitness trade-off in expressions
• Overcome policy gradient tail barriers

Innovation

• Decoder-only architecture with frequency-domain attention
• BIC-based reward for complexity-fitness trade-off
• Ranking-based weighted policy update method