Taylor Expansion Approximations for Dynamic Programming Problems

服务和制造环境中的操作决策通常要求决策对可用资源和系统特征的实时变化做出响应。由于这些操作环境通常非常复杂，因此捕获系统的动态特性通常非常困难。该项目旨在通过提供一种结构化的方法来逼近动态决策问题，从而帮助决策者管理动态复杂性。该项目的成果将促进各种领域的业务方法，包括保健业务以及商品和服务的生产和分配。该项目将培养从事不同行业相关项目的研究生。本项目将利用Stein的方法为随机动态规划（DP）问题创建新的近似解技术。Stein的方法最近被用在排队模型的语境中，当用合适的布朗模型近似一个排队系统的性能时，它被用来约束误差。这个项目将把这种方法扩展到受控马尔可夫过程的研究，从而超越性能分析，进入优化。这项研究将产生一种结构化的近似方法，允许明确地检查真正的最优解（由Bellman方程捕获）和布朗控制问题的最优解（由Hamilton-Jacobi-Bellman方程捕获）之间的最优性差距。如果成功，该研究将导致具有“近最优性”明确保证的DP问题的计算效率逼近方法。该研究将推动对马尔可夫决策过程和布朗控制问题之间关系的数学理解，超越排队的背景

Operational decision-making in service and manufacturing environments often requires that decisions respond to real-time changes in available resources and system characteristics. Because these operating environments are generally quite complex, capturing the dynamic nature of the system is often very difficult. This project aims to help the decision maker manage dynamic complexity by offering a structured approach to the approximation of dynamic decision problems. The results of this project will advance operational methods in a variety of domains, including healthcare operations and production and distribution of goods and services. The project will educate graduate students engaged in a diverse set of industry-related programs.This project will utilize Stein's method to create novel approximate solution techniques for stochastic dynamic programing (DP) problems. Stein's method has recently been used in the context of queueing models to bound the error when approximating the performance of a queuing system by that of a suitable Brownian model. This project will extend that approach to the study of controlled Markov processes, thus moving beyond performance analysis and into optimization. The research will result in a structured approximation approach that allows for explicit examination of the optimality gap between the true optimal solution (as captured by the Bellman equation) and the optimal solution of a Brownian control problem (as captured by a Hamilton-Jacobi-Bellman equation). If successful, the research will lead to computationally efficient approximation methods for DP problems with explicit guarantees of "near optimality". The research will advance the mathematical understanding of the relationship between Markov decision processes and Brownian control problems beyond the context of queueing