Bayesian Decision Theory Applied to the Finite State Markov Decision Problem

Abstract

Ron Howard solved the Markov decision problem with perfect knowledge of all the transition probabilities and rewards. In a practical situation, the transition probabilities may not be known exactly. Therefore, the problem this research attacks is the Markov decision problem with uncertain transition probabilities. In the case of perfect knowledge, the decision that maximizes the expected reward or gain is chosen. When there is uncertainty in the transition probabilities, the gains become random variables. Therefore, Bayesian decision theory is applied to this problem. A loss function is defined and an a priori density is defined. Bayes' formula and the loss function are used to compute a risk for each decision. The decision that minimizes the risk is chosen.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1972
Accession Number
AD0755797

Entities

People

  • William R. Osgood

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Bibliographies
  • Computer Simulations
  • Computers
  • Convergence
  • Convex Sets
  • Decision Theory
  • Equations
  • Identities
  • Markov Chains
  • Notation
  • Probability
  • Probability Distributions
  • Random Variables
  • Steady State
  • Theorems
  • Theses

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms