Abstraction Methods for Game Theoretic Poker
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Playing large games using simple strategies
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A polynomial-time nash equilibrium algorithm for repeated games
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Equivalence notions and model minimization in Markov decision processes
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
An algebraic approach to abstraction in reinforcement learning
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On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
A Texas Hold'em poker player based on automated abstraction and real-time equilibrium computation
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Lossless abstraction of imperfect information games
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
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AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Methods for empirical game-theoretic analysis
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
A sparse sampling algorithm for near-optimal planning in large Markov decision processes
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Approximating game-theoretic optimal strategies for full-scale poker
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
Probabilistic state translation in extensive games with large action sets
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Polynomial-time computation of exact correlated equilibrium in compact games
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Strategy purification and thresholding: effective non-equilibrium approaches for playing large games
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Near-optimal continuous patrolling with teams of mobile information gathering agents
Artificial Intelligence
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Abstraction followed by equilibrium finding has emerged as the leading approach to solving games. Lossless abstraction typically yields games that are still too large to solve, so lossy abstraction is needed. Unfortunately, prior lossy game abstraction algorithms have no guarantees on solution quality. We developed a framework that enables the design of lossy game abstraction algorithms with guarantees on solution quality. It simultaneously handles state and action abstraction. We define a measure of reward approximation error and transition probability error achieved by state and action abstraction in stochastic games such that the regret of the equilibrium found in the abstract game when implemented in the original, unabstracted game is upper-bounded by a function of those measures. We then develop the first lossy game abstraction algorithms with bounds on solution quality. Both of them work level-by-level up from the end of the game. One of the algorithms is greedy and the other is an integer linear program. We also prove that the abstraction problem is NP-complete (even with just action abstraction, 2 agents, and a 1-step game), but point out that this does not mean that the game abstraction problems that occur in practice cannot be solved quickly.