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Learning average reward irreducible stochastic games

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Material Information

Title:
Learning average reward irreducible stochastic games analysis and applications
Physical Description:
Book
Language:
English
Creator:
Li, Jun, 1974-
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla.
Publication Date:

Subjects

Subjects / Keywords:
stochastic approximation
reinforcement learning
power market
matrix game
markov decision processes
Dissertations, Academic -- Industrial Engineering -- Doctoral -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: A large class of sequential decision making problems under uncertainty with multiple competing decision makers/agents can be modeled as stochastic games. Stochastic games having Markov properties are called Markov games or competitive Markov decision processes. This dissertation presents an approach to solve non cooperative stochastic games, in which each decision maker makes her/his own decision independently and each has an individual payoff function. In stochastic games, the environment is nonstationary and each agent's payoff is affected by joint decisions of all agents, which results in the conflict of interest among the decision makers. In this research, the theory of Markov decision processes (MDPs) is combined with the game theory to analyze the structure of Nash equilibrium for stochastic games. In particular, the Laurent series expansion technique is used to extend the results of discounted reward stochastic games to average reward stochastic games. As a result, auxiliary matrix games are developed that have equivalent equilibrium points and values to a class of stochastic games that are irreducible and have average reward performance metric. R-learning is a well known machine learning algorithm that deals with average reward MDPs. The R-learning algorithm is extended to develop a Nash-R reinforcement learning algorithm for obtaining the equivalent auxiliary matrices. A convergence analysis of the Nash-R algorithm is developed from the study of the asymptotic behavior of its two time scale stochastic approximation scheme, and the stability of the associated ordinary differential equations (ODEs). The Nash-R learning algorithm is tested and then benchmarked with MDP based learning methods using a well known grid game. Subsequently, a real life application of stochastic games in deregulated power market is explored. According to the current literature, Cournot, Bertrand, and Supply Function Equilibrium (SFEs) are the three primary equilibrium models that are used to evaluate the power market designs. SFE is more realistic for pool type power markets. However, for a complicated power system, the convex assumption for optimization problems is violated in most cases, which makes the problems more difficult to solve. The SFE concept in adopted in this research, and the generators' behaviors are modeled as a stochastic game instead of one shot game. The power market is considered to have features such as multi-settlement (bilateral, day-ahead market, spot markets and transmission congestion contracts), and demand elasticity. Such a market consisting of multiple competing suppliers (generators) is modeled as a competitive Markov decision processes and is studied using the Nash-R algorithm.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2003.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Jun Li.
General Note:
Includes vita.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 111 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001441463
oclc - 54018149
notis - AJM5903
usfldc doi - E14-SFE0000136
usfldc handle - e14.136
System ID:
SFS0024832:00001


This item is only available as the following downloads:


Full Text
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ABSTRACT: A large class of sequential decision making problems under uncertainty with multiple competing decision makers/agents can be modeled as stochastic games. Stochastic games having Markov properties are called Markov games or competitive Markov decision processes. This dissertation presents an approach to solve non cooperative stochastic games, in which each decision maker makes her/his own decision independently and each has an individual payoff function. In stochastic games, the environment is nonstationary and each agent's payoff is affected by joint decisions of all agents, which results in the conflict of interest among the decision makers. In this research, the theory of Markov decision processes (MDPs) is combined with the game theory to analyze the structure of Nash equilibrium for stochastic games. In particular, the Laurent series expansion technique is used to extend the results of discounted reward stochastic games to average reward stochastic games. As a result, auxiliary matrix games are developed that have equivalent equilibrium points and values to a class of stochastic games that are irreducible and have average reward performance metric. R-learning is a well known machine learning algorithm that deals with average reward MDPs. The R-learning algorithm is extended to develop a Nash-R reinforcement learning algorithm for obtaining the equivalent auxiliary matrices. A convergence analysis of the Nash-R algorithm is developed from the study of the asymptotic behavior of its two time scale stochastic approximation scheme, and the stability of the associated ordinary differential equations (ODEs). The Nash-R learning algorithm is tested and then benchmarked with MDP based learning methods using a well known grid game. Subsequently, a real life application of stochastic games in deregulated power market is explored. According to the current literature, Cournot, Bertrand, and Supply Function Equilibrium (SFEs) are the three primary equilibrium models that are used to evaluate the power market designs. SFE is more realistic for pool type power markets. However, for a complicated power system, the convex assumption for optimization problems is violated in most cases, which makes the problems more difficult to solve. The SFE concept in adopted in this research, and the generators' behaviors are modeled as a stochastic game instead of one shot game. The power market is considered to have features such as multi-settlement (bilateral, day-ahead market, spot markets and transmission congestion contracts), and demand elasticity. Such a market consisting of multiple competing suppliers (generators) is modeled as a competitive Markov decision processes and is studied using the Nash-R algorithm.
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