主题：Data-Driven Contextual Optimization with Gaussian Mixtures: Flow-Based Generalization, Robust Models, and Multistage Extensions

基于高斯混合模型的数据驱动情景优化：流式泛化、鲁棒模型与多阶段扩展

时间: 2025年12月3日 晚上10点（线上）

地点：Zoom会议：734 4915 0855

主讲人：Prof. Grani A. Hanasusanto, University of Illinois Urbana-Champaign

Bio: Grani A. Hanasusanto is an Associate Professor and ISE Faculty Fellow at the University of Illinois Urbana-Champaign (UIUC). He is a faculty member in the Department of Industrial & Enterprise Systems Engineering and is affiliated with the Coordinated Science Laboratory. Previously, he was an Assistant Professor at The University of Texas at Austin and a Postdoctoral Scholar at École Polytechnique Fédérale de Lausanne. He holds a PhD in Operations Research from Imperial College London and an MSc in Financial Engineering from the National University of Singapore. Grani’s research focuses on developing tractable solution methodologies for decision-making under uncertainty, with applications spanning operations management, energy systems, finance, machine learning, and data analytics. His work has appeared in leading journals, including Operations Research, Mathematical Programming, SIAM Journal on Optimization, Manufacturing & Service Operations Management, Stochastic Systems, Transportation Research, and IEEE Transactions on Power Systems. He received the NSF CAREER Award in 2018 and was named a Walker Scholar by the UT Walker Department of Mechanical Engineering in recognition of his contributions to research, teaching, and service. He currently serves as an Associate Editor for Operations Research.

Abstract: Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of distributions. The inherent complexity of such structures often precludes an explicit functional relationship between the contextual information and the uncertain parameters, limiting the direct applicability of parametric models. Conversely, while non-parametric models offer greater representational flexibility, they are plagued by the "curse of dimensionality," leading to unsatisfactory performance in high-dimensional problems. To address these challenges, this paper proposes a novel contextual optimization framework based on Gaussian Mixture Models (GMMs). This model naturally bridges the gap between parametric and non-parametric approaches, inheriting the favorable sample complexity of parametric models while retaining the expressiveness of non-parametric schemes. By employing normalizing flows, we further relax the GM assumption and extend our framework to arbitrary distributions. Finally, inspired by the structural properties of GMMs, we design a novel GMM-based solution scheme for multistage stochastic optimization problems with Markovian uncertainty. This method exhibits significantly better sample complexity compared to traditional approaches, offering a powerful methodology for solving long-horizon, high-dimensional multistage problems. We demonstrate the effectiveness of our framework through extensive numerical experiments on a series of operations management problems. The results show that our proposed approach consistently outperforms state-of-the-art methods, underscoring its practical value for complex decision-making problems under uncertainty.