Fearnley, John (2010) Strategy iteration algorithms for games and Markov decision processes. PhD thesis, University of Warwick.

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Abstract

In this thesis, we consider the problem of solving two player infinite games,
such as parity games, mean-payoff games, and discounted games, the problem of
solving Markov decision processes. We study a specific type of algorithm for solving
these problems that we call strategy iteration algorithms. Strategy improvement
algorithms are an example of a type of algorithm that falls under this classification.
We also study Lemke’s algorithm and the Cottle-Dantzig algorithm, which
are classical pivoting algorithms for solving the linear complementarity problem.
The reduction of Jurdzinski and Savani from discounted games to LCPs allows these
algorithms to be applied to infinite games [JS08]. We show that, when they are
applied to games, these algorithms can be viewed as strategy iteration algorithms.
We also resolve the question of their running time on these games by providing a
family of examples upon which these algorithm take exponential time.
Greedy strategy improvement is a natural variation of strategy improvement,
and Friedmann has recently shown an exponential lower bound for this algorithm
when it is applied to infinite games [Fri09]. However, these lower bounds do not
apply for Markov decision processes. We extend Friedmann’s work in order to prove
an exponential lower bound for greedy strategy improvement in the MDP setting.
We also study variations on strategy improvement for infinite games. We
show that there are structures in these games that current strategy improvement
algorithms do not take advantage of. We also show that lower bounds given by
Friedmann [Fri09], and those that are based on his work [FHZ10], work because they
exploit this ignorance. We use our insight to design strategy improvement algorithms
that avoid poor performance caused by the structures that these examples use.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Game theory, Markov processes, Iterative methods (Mathematics)
Official Date:	August 2010
Dates:	Date Event August 2010 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jurdziński, Marcin ; Lazić, Ranko
Extent:	ix, 215 leaves : ill.
Language:	eng

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