用大模型自动设计优化任务特征，提升求解效率。
FunL2O: LLM-Guided Feature Function Design for Learning to Optimize
- 让大模型生成可执行的特征函数，替代人工设计。
- 在多种优化任务中，自动生成特征表现优于手工特征。
- 适合想自动化求解器特征设计的研究者和工程师。
学习型优化（L2O）通过训练模型预测解、热启动或分支决策等方式加速重复优化。然而，将问题实例映射为机器学习输入的特征函数这一关键环节，长期依赖人工设计，难以跨领域复用。本文提出 FunL2O，首个基于大模型驱动程序演化的统一框架，用于自动化特征设计。在类似 FunSearch 的循环中，大模型生成可执行的特征函数，固定评估流程则重新训练原 L2O 模型并测量下游优化性能。我们在线性与二次规划任务（涉及解预测和热启动）以及混合整数优化任务（使用 GNN 引导的后门分支和预测-搜索策略）上进行评估。结果表明，在连续与离散优化任务中，四种大模型生成的特征均持续优于手工特征。这验证了大模型驱动特征演化在 L2O 中通用且高效，为自动化表示设计提供了新范式。
原文摘要 · Abstract (English)
Learning-to-optimize (L2O) methods accelerate repeated optimization by training models to predict solutions, warm starts, branching decisions, or other forms of solver guidance. A critical yet largely overlooked component of these pipelines is the feature function that maps problem instances to inputs for machine learning models. Existing L2O methods typically rely on hand-crafted features, making representation design manual and largely fixed across domains. We introduce FunL2O, the first unified framework for automating feature design through LLM-driven program evolution for L2O. In a FunSearch-style loop, an LLM proposes executable feature functions, while a fixed evaluation process retrains the original L2O model and measures downstream optimization performance. We evaluate FunL2O on linear and quadratic programming tasks involving solution prediction and warm-starting, as well as on mixed-integer optimization tasks using GNN-guided backdoor branching and Predict-and-Search. Across continuous and discrete optimization tasks and four LLMs, the evolved features consistently outperform hand-crafted representations. These results establish LLM-driven feature evolution as a general and effective approach to automating representation design in L2O.
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