FunL2O：面向学习优化的大语言模型引导特征函数设计
FunL2O: LLM-Guided Feature Function Design for Learning to Optimize
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中文总结 AI 辅助
该研究提出首个大语言模型驱动特征自动化设计的L2O统一框架FunL2O，经多类优化任务及四种大语言模型验证，其演化特征性能优于人工设计特征。
中文摘要 AI 辅助
学习优化（L2O）方法通过训练模型预测解、热启动、分支决策或其他形式的求解器引导，来加速重复优化过程。这些流程中一个关键却基本被忽视的组件是特征函数，它将问题实例映射为机器学习模型的输入。现有L2O方法通常依赖人工设计的特征，导致表示设计需手动完成且跨领域基本固定。我们提出FunL2O，首个通过大语言模型驱动的程序演化实现L2O特征自动化设计的统一框架。在类FunSearch的循环中，大语言模型提出可执行的特征函数，而固定的评估流程会重新训练原始L2O模型并测量下游优化性能。我们在涉及解预测和热启动的线性与二次规划任务，以及使用GNN引导后门分支和预测-搜索的混合整数优化任务上评估FunL2O。在连续和离散优化任务及四种大语言模型上，演化出的特征始终优于人工设计的表示。这些结果证明，大语言模型驱动的特征演化是L2O中表示设计自动化的通用且有效方法。
英文摘要
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.
