报告题目：Beyond Linear Decision Rules: LLM-Guided Basis Function Discovery for Data-Driven Optimization
报告人：赵越 助理教授
邀请人：边博旻 教授
报告时间及地点：2026.06.29 14:00-15:30 经管学院B208
报告人简况：
Zhao Yue, Assistant Professor at Peking University HSBC Business School, he holds a Ph.D. in Operations Research from the National University of Singapore. His primary research areas include data-driven optimization, robust analytics, and LLM for decision-making with applications in supply chain, logistics, and socially responsible operations. He has publications in top business journals such as Management Science, Operations Research, and INFORMS Journal on Computing.
报告内容摘要：
Stochastic optimization often restricts recourse decisions to affine parameterizations for computational tractability, potentially creating a substantial and irreducible approximation gap. Large language models (LLMs) offer new opportunities to discover richer problem-specific structures that can help narrow this gap. We propose Generative Stochastic Optimization (GenSO), a framework that uses LLMs to discover adaptive policy representations while preserving the rigor and tractability of optimization models. The key component of GenSO is the Generative Linear Decision Rule (GenLDR), in which recourse decisions are expressed as linear combinations of closed-form nonlinear basis functions generated by LLMs from problem structure and domain knowledge. Consequently, GenSO increases policy expressiveness without compromising tractability and interpretability. We establish finite-sample guarantees for fixed generated bases and further derive a performance bound under a hit-probability model motivated by empirical scaling laws of LLMs. We evaluate GenSO on a multi-period newsvendor problem and a data center location problem with multi-period job scheduling calibrated using real-world datasets. Across both settings, GenSO consistently outperforms existing benchmarks in out-of-sample evaluations while uncovering interpretable nonlinear decision structures that are difficult to identify through conventional manual design.
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