Taylor Expansion Approximations for Dynamic Programming Problems

动态规划问题的泰勒展开近似

• 批准号: 1662294
• 负责人: Itai Gurvich
• 金额: $ 35万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-06-01 至 2020-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1662294&HistoricalAwards=false
• 关键词: Taylor; Expansion; Approximations; Dynamic; Programming

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

服务和制造环境中的运营决策通常要求决策对可用资源和系统特性的实时变化做出响应。由于这些操作环境通常相当复杂，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近似动态决策问题，以帮助决策者管理动态复杂性。该项目的成果将推动各个领域的业务方法，包括医疗保健业务以及商品和服务的生产和分销。该项目将教育研究生从事一系列不同的行业相关的程序。该项目将利用斯坦的方法来创建随机动态规划（DP）问题的新的近似解技术。Stein的方法最近被用于排队模型的上下文中，以限制当通过合适的布朗模型来近似排队系统的性能时的误差。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。该研究将导致一个结构化的近似方法，允许显式检查真正的最优解（由贝尔曼方程捕获）和布朗控制问题的最优解（由汉密尔顿-雅可比-贝尔曼方程捕获）之间的最优性差距。如果成功，研究将导致计算效率的近似方法DP问题的明确保证“近最优”。该研究将推进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，而不仅仅局限于马尔可夫决策过程

项目成果

On the Taylor Expansion of Value Functions

• DOI: 10.1287/opre.2019.1903
• 发表时间: 2018-04
• 期刊: Oper. Res.
• 作者: Anton Braverman;I. Gurvich;Jun-fei Huang

Beyond Heavy-Traffic Regimes: Universal Bounds and Controls for the Single-Server Queue

超越大流量制度：单服务器队列的通用边界和控制

• DOI: 10.1287/opre.2017.1715
• 发表时间: 2018
• 期刊: Operations Research
• 影响因子: 2.7
• 作者: Huang, Junfei;Gurvich, Itai
• 通讯作者: Gurvich, Itai