Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning
<|reference_start|>Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning: 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.<|reference_end|>
@article{chen2024symbol:,
    title={Symbol: Generating Flexible Black-Box Optimizers through Symbolic
  Equation Learning},
    author={Jiacheng Chen, Zeyuan Ma, Hongshu Guo, Yining Ma, Jie Zhang, Yue-Jiao
  Gong},
    journal={arXiv preprint arXiv:2402.02355},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02355},
    primaryClass={cs.LG cs.NE}
}