发表机构
Massachusetts Institute of Technology; Microsoft Research（麻省理工学院; 微软研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
TACIT结合LLM推理与优化形式化，通过自上而下和自下而上两种范式自动修复错误指定的优化模型，在38个场景中修复率达78.9%，优于基线。
AI 中文摘要
现实世界的优化问题难以精确建模，因为许多目标和约束存在于领域专家的隐性知识中，使其难以形式化。因此，优化模型常常包含校准不当的目标、缺失的约束或遗漏的决策变量，导致解决方案无法反映运营实际。我们通过利用由历史解决方案和后续用户覆盖组成的历史数据，自动修复错误指定的公式来应对这一挑战。传统方法如逆优化和约束学习往往过拟合稀疏数据并产生复杂公式。我们的核心思想是将LLM的推理能力和先验知识与优化提供的正式基础相结合。我们通过两种互补范式实现这一思想。自上而下，LLM提出结构性修复，包括新的约束和变量，其数值参数通过优化进行校准和验证。自下而上，优化从观察到的决策中推断切割，LLM将其情境化为可解释、可泛化的建模约束。我们在涵盖九类优化问题的38个错误指定场景上评估了我们的方法，其中几个来自实际应用，并表明TACIT可以修复其中78.9%的问题（而最佳基线为60.5%）。
英文摘要
Real-world optimization problems are difficult to model accurately because many objectives and constraints reside in domain experts' tacit knowledge, making them hard to formalize. As a result, optimization models often contain miscalibrated objectives, missing constraints, or omitted decision variables, leading to solutions that fail to reflect operational realities. We address this challenge by automatically repairing misspecified formulations using historical data consisting of past solutions and subsequent user overrides. Traditional approaches such as inverse optimization and constraint learning tend to overfit sparse data and produce complex formulations. Our central idea is to combine the reasoning capabilities and prior knowledge of LLMs with the formal grounding provided by optimization. We realize this idea through two complementary paradigms. Top-down, an LLM proposes structural repairs, including new constraints and variables, whose numerical parameters are calibrated and validated through optimization. Bottom-up, optimization infers cuts from observed decisions, which the LLM contextualizes into interpretable, generalizable modeling constraints. We evaluate our approach on 38 misspecification scenarios spanning nine classes of optimization problems, several drawn from real-world applications, and show that TACIT can repair 78.9% of them (vs. 60.5% for the best baseline).
