Symbolic Learning to Optimize: Towards Interpretability and Scalability

TL;DR

This paper introduces a symbolic regression approach to Learning to Optimize (L2O), enhancing interpretability and scalability, and presents a lightweight, meta-trainable optimizer that outperforms traditional methods on large-scale problems.

Contribution

It pioneers the integration of symbolic regression into L2O, providing a new framework for interpretability and scalability, and develops a lightweight, effective optimizer.

Findings

Symbolic L2O models are more interpretable than neural network-based models.

The proposed model outperforms human-designed optimizers on large-scale tasks.

The framework enables scalable and explainable optimization solutions.

Abstract

Recent studies on Learning to Optimize (L2O) suggest a promising path to automating and accelerating the optimization procedure for complicated tasks. Existing L2O models parameterize optimization rules by neural networks, and learn those numerical rules via meta-training. However, they face two common pitfalls: (1) scalability: the numerical rules represented by neural networks create extra memory overhead for applying L2O models, and limit their applicability to optimizing larger tasks; (2) interpretability: it is unclear what an L2O model has learned in its black-box optimization rule, nor is it straightforward to compare different L2O models in an explainable way. To avoid both pitfalls, this paper proves the concept that we can "kill two birds by one stone", by introducing the powerful tool of symbolic regression to L2O. In this paper, we establish a holistic symbolic representation and analysis framework for L2O, which yields a series of insights for learnable optimizers. Leveraging our findings, we further propose a lightweight L2O model that can be meta-trained on large-scale problems and outperformed human-designed and tuned optimizers. Our work is set to supply a brand-new perspective to L2O research. Codes are available at: https://github.com/VITA-Group/Symbolic-Learning-To-Optimize.