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Decision Processes in Dynamic Probabilistic Systems A.V. Gheorghe

Decision Processes in Dynamic Probabilistic Systems By A.V. Gheorghe

Decision Processes in Dynamic Probabilistic Systems by A.V. Gheorghe


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Decision Processes in Dynamic Probabilistic Systems Summary

Decision Processes in Dynamic Probabilistic Systems by A.V. Gheorghe

'Et moi *...* si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf next Jules Verne (0 the dusty canister labelled 'discarded non- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Table of Contents

1 Semi-Markov and Markov Chains.- 1.1 Definitions and basic properties.- 1.2 Algebraic and analytical methods in the study of Markovian systems.- 1.3 Transient and recurrent processes.- 1.4 Markovian populations.- 1.5 Partially observable Markov chains.- 1.6 Rewards and discounting.- 1.7 Models and applications.- 1.8 Dynamic-decision models for clinical diagnosis.- 2 Dynamic and Linear Programming.- 2.1 Discrete dynamic programming.- 2.2 A linear programming formulation and an algorithm for computation.- 3 Utility Functions and Decisions under Risk.- 3.1 Informational lotteries and axioms for utility functions.- 3.2 Exponential utility functions.- 3.3 Decisions under risk and uncertainty; event trees.- 3.4 Probability encoding.- 4 Markovian Decision Processes (Semi-Markov and Markov) with Complete Information (Completely Observable).- 4.1 Value iteration algorithm (the finite horizon case).- 4.2 Policy iteration algorithm (the finite horizon optimization).- 4.3 Policy iteration with discounting.- 4.4 Optimization algorithm using linear programming.- 4.5 Risk-sensitive decision processes.- 4.6 On eliminating sub-optimal decision alternatives in Markov and semi-Markov decision processes.- 5 Partially Observable Markovian Decision Processes.- 5.1 Finite horizon partially observable Markov decision processes.- 5.2 The infinite horizon with discounting for partially observable Markov decision processes.- 5.3 A useful policy iteration algorithm, for discounted (? < 1) partially observable Markov decision processes.- 5.4 The infinite horizon without discounting for partially observable Markov processes.- 5.5 Partially observable semi-Markov decision processes.- 5.6 Risk-sensitive partially observable Markov decision processes.- 6 Policy Constraints in Markov DecisionProcesses.- 6.1 Methods of investigating policy costraints in Markov decision processes.- 6.2 Markov decision processes with policy constraints.- 6.3 Risk-sensitive Markov decision process with policy constraints.- 7 Applications.- 7.1 The emergency repair control for electrical power systems.- 7.2 Stochastic models for evaluation of inspection and repair schedules [2].- 7.3 A Markovian dicision model for clinical diagnosis and treatment applied to the respiratory system.

Additional information

NPB9780792305446
9780792305446
0792305442
Decision Processes in Dynamic Probabilistic Systems by A.V. Gheorghe
New
Hardback
Springer
1990-07-31
376
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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