题　目：Leveraging Nondegeneracy in Dynamic Resource Allocation

嘉　宾：张经纬 助理教授 香港中文大学（深圳）

主持人：许欢 教授 上海交通大学安泰经济与管理学院

时　间：2025年9月18日（周四）14:00-15:30

地　点：安泰楼A507室

内容简介：

Sequential decision problems often involve allocating shared resources across a set of independent systems over time. A classic example is the restless bandit problem, constrained by a budget that limits arm selection. This problem finds applications in various areas, such as inventory management, dynamic pricing and hospital care scheduling. Fluid relaxations provide a natural approximation technique for this broad class of problems, transforming the original discrete stochastic problem into a more tractable deterministic one. Recent advancements have established strong performance guarantees for policies derived from fluid relaxations, which can be categorized into two main types: those addressing homogeneous subproblems and those addressing heterogeneous subproblems. For homogeneous subproblems, a celebrated ξO(1)ξ optimality gap has been established, assuming certain nondegeneracy conditions are met. However, this theoretical guarantee often requires the number of subproblems ξNξ to be sufficiently large relative to the degree of nondegeneracy, and it deteriorates to ξO(N)ξ as the degree of nondegeneracy approaches zero. In contrast, for heterogeneous subproblems, policies have been developed that achieve performance within ξO(\sqrt{N｝)ξ of optimal, without accounting for nondegeneracy effects. This paper aims to unify and enhance these recent performance results. We develop a \emph{fluid-budget balancing｝ policy that balances the trade-offs from deviating from the optimal fluid path. Our policy leverages the strengths of both homogeneous and heterogeneous approaches, ensuring robust performance across a wide range of scenarios. We demonstrate that our policy achieves an optimality gap within ξO(\exp(-\deltaˆ2 N)\min\{\sqrt{N｝,\deltaˆ{-1｝\｝)ξ, where ξ\delta\ge 0ξ quantifies the degree of nondegeneracy. This policy maintains an ξO(\sqrt{N｝)ξ optimality gap in the worst scenario when the fluid relaxation is degenerate, improving smoothly to ξO(1)ξ as the degree of nondegeneracy increases, regardless of the heterogeneity of subproblems. We demonstrate the application of our policies on a dynamic multi-warehouse inventory problem and find, numerically, that our policy achieves excellent performance, outperforming the widely used fluid policy, as our theory suggests.

演讲人简介：

Jingwei Zhang is an Assistant Professor in the School of Data Science at The Chinese University of Hong Kong, Shenzhen. His research focuses on developing stochastic models and analytical methods for decision-making problems under uncertainty, with applications in resource allocation, revenue management, and assortment optimization. His work has been published in Operations Research. Prior to joining CUHK-Shenzhen, he was a postdoctoral researcher at Columbia Business School. He received his Ph.D. in Decision Sciences from Duke University in 2022.

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