发表机构
The Hong Kong Polytechnic University; University of Colorado Boulder（香港理工大学; 科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出 OSCAR 框架，利用离线模拟器认证改进，在多个 LLM 间按成本排序分配尝试，以低成本生成准确优化模型，并在五个基准上实现高准确率。
AI 中文摘要
大型语言模型可以将业务描述翻译为优化模型，但可执行代码可能错误地表示约束或目标。求解器随后可能针对错误的问题返回最优解。即使解满足预期的操作规则，也可能存在更好的方案。对于反复使用优化建模的组织，基于 LLM 的框架应以低成本生成准确的公式，并且理想情况下可在本地运行。我们研究如何验证改进以及在价格和能力不同的 LLM 之间分配尝试。我们开发了 OSCAR（通过模拟器、编码器和审查器进行优化建模），它使用针对标记决策示例认证的离线模拟器来比较候选方案，并在可行性之外继续搜索。我们将搜索下一个经认证的改进建模为在未观测难度下的顺序决策：调用哪些 LLM 以及何时停止。在简化的已知先验设置中，我们给出了成本排序升级为最优的条件。对于一般菜单，我们推导出无先验的竞争性保证。在五个基准问题上，OSCAR 在报告的设置下使用两个小型开放权重 LLM 实现了 95% 至 100% 的准确率，每个模型均可在单个 GPU 上本地部署。它们的单次尝试准确率平均为 29% 和 48%。在每个问题运行五次的情况下，Codex 和 Claude Code 的平均 token 成本分别是 OSCAR 的 3.1 倍和 5.8 倍。OSCAR 支持在本地或云端使用开放权重模型，具体取决于预算和保密要求。企业应维护可行和不可行决策的标记决策示例，以澄清平实语言的操作规则。当 LLM 的解释与这些标签冲突时，OSCAR 遵循这些标签。随着 LLM 能力和价格的变化，OSCAR 的简单操作规则和可调整设置帮助企业适应其模型选择并受益于这些进展。
英文摘要
Large language models can translate business descriptions into optimization models, but executable code may misrepresent constraints or objectives. A solver can then return an optimal solution to the wrong problem. Even when the solution satisfies the intended operating rules, a better plan may exist. For organizations that repeatedly use optimization modeling, an LLM-based framework should produce accurate formulations at low cost and, ideally, run locally. We study how to verify improvements and allocate attempts across LLMs that differ in price and capability. We develop OSCAR (Optimization modeling by Simulator, Coder, And Reviewer), which uses an offline Simulator certified against labeled decision examples to compare candidates and continues searching beyond feasibility. We model the search for the next certified improvement as sequential decisions under unobserved difficulty: which LLMs to call and when to stop. In a simplified known-prior setting, we give conditions under which cost-ordered escalation is optimal. For general menus, we derive a prior-free competitive guarantee. On five benchmark problems, OSCAR achieves 95% to 100% accuracy at the reported settings using two small open-weight LLMs, each deployable locally on a single GPU. Their single-attempt accuracies average 29% and 48%. In five runs per problem, Codex and Claude Code incur average token costs 3.1 and 5.8 times OSCAR's, respectively. OSCAR supports open-weight models locally or in the cloud, depending on budget and confidentiality requirements. Firms should maintain labeled decision examples of feasible and infeasible decisions to clarify plain-language operating rules. OSCAR follows these labels when an LLM's interpretation conflicts with them. As LLM capabilities and prices change, OSCAR's simple operating rules and adjustable settings help firms adapt their model choices and benefit from these advances.
