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Constrained Markov Decision Processes 1st edition
  • 2020-04-10
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    ###-Book Description Begin-###
    -------如果这里没有任何信息,不是真没有,是我们懒!请复制书名上amazon搜索书籍信息。-------

    Constrained Markov Decision Processes

    Constrained Markov Decision Processes 1st edition.jpg


    1st Edition


    By Eitan Altman

    Chapman and Hall/CRC

    256 pages

    Table of Contents

    INTRODUCTION

    Examples of Constrained Dynamic Control Problems

    On Solution Approaches for CMDPs with Expected Costs

    Other Types of CMDPs

    Cost Criteria and Assumptions

    The Convex Analytical Approach and Occupation Measures

    Linear Programming and Lagrangian Approach for CMDPs

    About the Methodology

    The Structure of the Book

    PART ONE: FINITE MDPS

    MARKOV DECISION PROCESSES

    The Model

    Cost Criteria and the Constrained Problem

    Some Notation

    The Dominance of Markov Policies

    THE DISCOUNTED COST

    Occupation Measure and the Primal LP

    Dynamic Programming and Dual LP: the Unconstrained Case

    Constrained Control: Lagrangian Approach

    The Dual LP

    Number of Randomizations

    THE EXPECTED AVERAGE COST

    Occupation Measure and the Primal LP

    Equivalent Linear Program

    The Dual Program

    Number of Randomizations

    FLOW AND SERVICE CONTROL IN A SINGLE-SERVER QUEUE

    The Model

    The Lagrangian

    The Original Constrained Problem

    Structure of Randomization and Implementation Issues

    On Coordination Between Controllers

    Open Questions

    PART TWO: INFINITE MDPS

    MDPS WITH INFINITE STATE AND ACTION SPACES

    The Model

    Cost Criteria

    Mixed Policies, and Topologic Structures

    The Dominance of Markov Policies

    Aggregation of States

    Extra Randomization in the Policies

    Equivalent Quasi-Markov Model and Quasi-Markov Policies

    THE TOTAL COST: CLASSIFICATION OF MDPS

    Transient and Absorbing MDPs

    MDPs With Uniform Lyapunov Functions

    Equivalence of MDP With Unbounded and bounded costs

    Properties of MDPs With Uniform Lyapunov Functions

    Properties for Fixed Initial Distribution

    Examples of Uniform Lyapunov Functions

    Contracting MDPs

    THE TOTAL COST: OCCUPATION MEASURES AND THE PRIMAL LP

    Occupation Measure

    Continuity of Occupation Measures

    More Properties of MDPs

    Characterization of Achievable Sets of Occupation Measure

    Relation Between Cost and Occupation Measure

    Dominating Classes of Policies

    Equivalent Linear Program

    The Dual Program

    THE TOTAL COST: DYNAMIC AND LINEAR PROGRAMMING

    Non-Constrained Control: Dynamic and Linear Programming

    Superharmonic Functions and Linear Programming

    Set of Achievable Costs

    Constrained Control: Lagrangian Approach

    The Dual LP

    State Truncation

    A Second LP Approach for Optimal Mixed Policies

    More on Unbound Costs

    THE DISCOUNTED COST

    The Equivalent Total Cost Model

    Occupation Measure and LP

    Non-negative Immediate Cost

    Weak Contracting Assumptions and Lyapunov Functions

    Example: Flow and Service Control

    THE EXPECTED AVERAGE COST

    Occupation Measures

    Completeness Properties of Stationary Policies

    Relation Between Cost and Occupation Measure

    Dominating Classes of Policies

    Equivalent Linear Program

    The Dual Program

    The Contracting Framework

    Other Conditions for the Uniform Integrability

    The Case of Uniform Lyapunov Conditions

    EXPECTED AVERAGE COST: DYNAMIC PROGRAMMING AND LP

    The Non-Constrained Case: Optimality Inequality

    Non-Constrained Control: Cost Bounded Below

    Dynamic Programming and Uniform Lyapunov Function

    Super-Harmonic Functions and Linear Programming

    Set of Achievable Costs

    Constrained Control: Lagrangian Approach

    The Dual LP

    A Second LP Approach for Optimal Mixed Policies

    PART THREE: ASYMPTOTIC METHODS AND APPROXIMATIONS

    SENSITIVITY ANALYSIS

    Introduction

    Approximation of the Values

    Approximation and Robustness of the Policies

    CONVERGENCE OF DISCOUNTED CONSTRAINED MDPS

    Convergence in the Discount Factor

    Convergence to the Expected Average Cost

    The Case of Uniform Lyapunov Function

    CONVERGENCE AS THE HORIZON TENDS TO INFINITY

    The Discounted Cost

    The Expected Average Cost: Stationary Policies

    The Expected Average Cost: General Policies

    STATE TRUNCATION AND APPROXIMATION

    The Approximating sets of States

    Scheme I: the Total Cost

    Scheme II: the Total Cost

    Scheme III: the Total Cost

    The Expected Average Cost

    Infinite MDPs: on the Number of Randomizations

    APPENDIX: CONVERGENCE OF PROBABILITY MEASURES

    REFERENCES

    LIST OF SYMBOLS AND NOTATION

    INDEX



    ###-Book Description End-###
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