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

• URL: http://arxiv.org/abs/2402.02355v2
• Date: Wed, 7 Feb 2024 02:38:52 GMT
• Title: Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning
• Authors: Jiacheng Chen, Zeyuan Ma, Hongshu Guo, Yining Ma, Jie Zhang, Yue-Jiao Gong
• Abstract summary: We present textscSymbol, a framework that promotes the automated discovery of black-boxs through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated. Extensive experiments reveal that the generalizations generated by textscSymbol not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot abilities.
• Score: 16.338146844605404
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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