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Monte Carlo Sampling and Regret Minimization for Equilibrium Computation and Decision-Making in Large Extensive Form Games Open Access


Other title
regret minimization
extensive form game
game theory
Type of item
Degree grantor
University of Alberta
Author or creator
Lanctot, Marc
Supervisor and department
Michael Bowling (Computing Science)
Examining committee member and department
Michael Wellman (Computer Science & Engineering, University of Michigan)
Michael Bowling (Computing Science)
Csaba Szepesvari (Computing Science)
Joerg Sander (Computing Science)
Duane Szafron (Computing Science)
Martin Mueller (Computing Science)
Department of Computing Science

Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis, we investigate the problem of decision-making in large two-player zero-sum games using Monte Carlo sampling and regret minimization methods. We demonstrate four major contributions. The first is Monte Carlo Counterfactual Regret Minimization (MCCFR): a generic family of sample-based algorithms that compute near-optimal equilibrium strategies. Secondly, we develop a theory for applying counterfactual regret minimization to a generic subset of imperfect recall games as well as a lossy abstraction mechanism for reducing the size of very large games. Thirdly, we describe Monte Carlo Minimax Search (MCMS): an adversarial search algorithm based on *-Minimax that uses sparse sampling. We then present variance reduction techniques that can be used in these settings, with a focused application to Monte Carlo Tree Search (MCTS). We thoroughly evaluate our algorithms in practice using several different domains and sampling strategies.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
M. Lanctot, K. Waugh, M. Bowling, and M. Zinkevich. Sampling for regret minimization in extensive games. In Advances in Neural Information Processing Systems (NIPS 2009), 2009.M. Lanctot, R. Gibson, N. Burch, and M. Bowling. No-regret learning in extensive-form games with imperfect recall. In Proceedings of the Twenty-Ninth International Conference on Machine Learning (ICML 2012), 2012.M. Lanctot, A. Saffidine, J. Veness, and C. Archibald. Sparse sampling for adversarial games. In Proceedings of the ECAI Computer Games Workshop, pages 37-49, 2012.J. Veness, M. Lanctot, and M. Bowling. Variance reduction in Monte-Carlo tree search. In J. Shawe-Taylor, R.S. Zemel, P. Bartlett, F.C.N. Pereira, and K.Q. Wein- berger, editors, Advances in Neural Information Processing Systems 24, pages 1836-1844. 2011.

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