Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning

TL;DR

This paper introduces extsc{Symbol}, a framework that uses symbolic equation learning to automatically generate flexible, interpretable black-box optimizers that outperform existing methods and generalize well across diverse tasks.

Contribution

The paper proposes extsc{Symbol}, a novel symbolic equation learning framework for automated black-box optimizer discovery, surpassing state-of-the-art methods and demonstrating strong zero-shot generalization.

Findings

Generated optimizers outperform baselines

Exhibit strong zero-shot generalization

Showcase flexibility and interpretability

Abstract

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present \textsc{Symbol}, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within \textsc{Symbol}, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by \textsc{Symbol} not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our \textsc{Symbol} framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.