Turnpike Phenomenon for Markov Decision Processes
暫譯: 馬可夫決策過程中的高速公路現象

Zaslavski, Alexander J.

Turnpike Phenomenon for Markov Decision Processes
  • 出版商: Springer
  • 出版日期: 2025-10-02
  • 售價: $2,570
  • 貴賓價: 9.5 折 $2,442
  • 語言: 英文
  • 頁數: 133
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032008530
  • ISBN-13: 9783032008534
  • 相關分類: Reinforcement

    • 海外代購書籍(需單獨結帳)

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商品描述

This book provides a comprehensive examination of the structure of approximate optimal policies in Markov decision processes (MDPs) with finite state spaces, as well as approximate optimal solutions for deterministic discrete-time optimal control problems. At its core, the monograph delves into the turnpike property, a concept introduced by P. Samuelson, which suggests that optimal solutions are largely determined by the objective function, independent of interval length or endpoint conditions.

Key concepts include the uniqueness and stability of minimizing Markov actions, the existence of overtaking optimal policies, and the asymptotic and weak turnpike properties. The authors meticulously examine these phenomena across various classes of MDPs, employing a Baire category approach to demonstrate the generic nature of these properties. The book also addresses the impact of perturbations on cost functions, ensuring the stability of turnpike properties.

This monograph is an essential resource for researchers and scholars in the fields of operations research, applied mathematics, and control theory. It provides valuable insights into the intricate dynamics of MDPs and optimal control systems, making it a must-read for anyone seeking to deepen their understanding of these complex topics.

商品描述(中文翻譯)

本書全面探討了有限狀態空間中的馬可夫決策過程（MDPs）中近似最優政策的結構，以及確定性離散時間最優控制問題的近似最優解。該專著的核心深入研究了由P. Samuelson提出的轉運性質（turnpike property），該概念表明，最優解主要由目標函數決定，與區間長度或端點條件無關。

關鍵概念包括最小化馬可夫行動的唯一性和穩定性、超越最優政策的存在，以及漸近和弱轉運性質。作者仔細檢視了這些現象在各類MDPs中的表現，採用Baire類別方法來展示這些性質的普遍性。本書還探討了擾動對成本函數的影響，確保轉運性質的穩定性。

這本專著是運籌學、應用數學和控制理論領域研究人員和學者的重要資源。它提供了對MDPs和最優控制系統複雜動態的寶貴見解，是任何希望深入理解這些複雜主題的讀者必讀的書籍。

作者簡介

Alexander J. Zaslavski is a senior researcher at the Technion - Israel Institute of Technology. He was born in Ukraine in 1957 and got his PhD in Mathematical Analysis in 1983 at the Institute of Mathematics, Novosibirsk. He is the author of 26 research monographs and more than 600 research papers and editor of more than 70 edited volumes and journals' special issues. He is the Founding Editor and Editor-in-Chief of the journal Pure and Applied Functional Analysis and Editor-in-Chief of journal Communications in Optimization Theory. His area of research contains nonlinear functional analysis, control theory, optimization, calculus of variations, dynamical systems theory, game theory and mathematical economics.

作者簡介(中文翻譯)

亞歷山大·J·扎斯拉夫斯基是以色列理工學院（Technion - Israel Institute of Technology）的高級研究員。他於1957年出生於烏克蘭，並於1983年在新西伯利亞數學研究所獲得數學分析博士學位。他是26本研究專著的作者，發表了超過600篇研究論文，並編輯了70多本編輯卷和期刊的特刊。他是《純粹與應用函數分析》（Pure and Applied Functional Analysis）期刊的創始編輯及主編，以及《優化理論通訊》（Communications in Optimization Theory）期刊的主編。他的研究領域包括非線性函數分析、控制理論、優化、變分法、動態系統理論、博弈論和數學經濟學。

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