Finite Approximations in Discrete-Time Stochastic Control

1. Front Matter

   Pages i-vii

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2. Introduction and Summary

   • Naci Saldi, Tamás Linder, Serdar Yüksel

   Pages 1-11

3. Finite Model Approximations in Stochastic Control

   1. Front Matter

      Pages 13-13

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   2. Prelude to Part I

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 15-21

   3. Finite-Action Approximation of Markov Decision Processes

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 23-48

   4. Finite-State Approximation of Markov Decision Processes

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 49-97

   5. Approximations for Partially Observed Markov Decision Processes

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 99-123

   6. Approximations for Constrained Markov Decision Problems

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 125-149

4. Finite Model Approximations in Decentralized Stochastic Control

   1. Front Matter

      Pages 151-151

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   2. Prelude to Part II

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 153-157

   3. Finite Model Approximations in Decentralized Stochastic Control

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 159-175

   4. Asymptotic Optimality of Finite Models for Witsenhausen’s Counterexample and Beyond

      • Naci Saldi, Tamás Linder, Serdar Yüksel

      Pages 177-188

5. Back Matter

   Pages 189-198

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In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. 


This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

• stochastic control
• decentralized stochastic control
• quantization
• numerical approximation
• finite state approximations
• Markov decision processes
• asymptotic optimality

“The book is very well written, with focus on clarity … . material of this monograph is pretty advanced, the presentation style is very clear, compact and relatively easy to follow, but at the same time mathematically rigorous. The monograph is a good piece of work on a subject that attracts considerable attention. Both researchers and professionals in applied mathematics will find this book very useful. It can also be recommended as a valuable reference text in approximate dynamic programming.” (Dariusz Uciński, zbMATH 1471.93005, 2021)

“This book is an interesting and complete treatise on finite approximations of different kinds of discrete-time stochastic control problems. It is based on several recent research results on the topic presented which have been published in various papers written by the authors.” (Raúl Montes-de-Oca, Mathematical Reviews, March, 2019)​

• Department of Natural and Mathematical Sciences, Ozyegin University, Istanbul, Turkey

  Naci Saldi

• Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

  Tamás Linder

• Department of Mathematics & Statistics, Queen’s University, Kingston, Canada

  Serdar Yüksel

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