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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.","url_abs":"https://arxiv.org/abs/2402.02355v2","url_pdf":"https://arxiv.org/pdf/2402.02355v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"symbol-generating-flexible-black-box","repo_url":"https://github.com/gmc-drl/symbol","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"meta-learning","task_name":"Meta-Learning"},{"task_slug":"zero-shot-generalization","task_name":"Zero-shot Generalization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2402.02355","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.02355"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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