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94
The Nonstochastic Multiarmed Bandit Problem
 SIAM JOURNAL OF COMPUTING
, 2002
"... In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the tradeoff between exploration (trying out ..."
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Cited by 491 (34 self)
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round payoff of the strategy at the rate O((logN)1/2T−1/2). Finally, we apply our results to the problem of playing an unknown repeated matrix game. We show that our algorithm approaches the minimax payoff of the unknown game at the rate O(T−1/2).
PerfectInformation Stochastic MeanPayoff Parity Games ⋆,⋆⋆
"... Abstract The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1 2player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other ..."
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, and the other transitions are determined probabilistically. We consider 2 1player games where the objec2 tive of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). We establish that the problem
Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All Lptype Problems
, 2007
"... We show that a Simple Stochastic Game (SSG) can be formulated as an LPtype problem. Using this formulation, and the known algorithm of Sharir and Welzl [SW] for LPtype problems, we obtain the first strongly subexponential solution for SSGs (a strongly subexponential algorithm has only been known ..."
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Cited by 23 (0 self)
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for binary SSGs [L]). Using known reductions between various games, we achieve the first strongly subexponential solutions for Discounted and Mean Payoff Games. We also give alternative simple proofs for the best known upper bounds for Parity Games and binary SSGs. To the best of our knowledge, the LP
Energy parity games
 PROC. OF LICS, IEEE COMPUTER SOCIETY
"... Energy parity games are infinite twoplayer turnbased games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own i ..."
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Cited by 60 (11 self)
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equivalent to the problem of deciding the winner in meanpayoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve meanpayoff parity games.
Solving Mean Payoff Parity Games With Strategy Improvement
, 2008
"... Two player games played on finite graphs have attracted much interest in the formal methods community. It has been shown that the problem of model checking the modal µcalculus is equivalent to the problem of solving a two player parity game [2]. In these games, each vertex is assigned an integer ..."
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Two player games played on finite graphs have attracted much interest in the formal methods community. It has been shown that the problem of model checking the modal µcalculus is equivalent to the problem of solving a two player parity game [2]. In these games, each vertex is assigned an inte
Evolution in Games with Randomly Disturbed Payoffs
 Journal of Economic Theory
, 2007
"... We consider a simple model of stochastic evolution in population games. In our model, each agent occasionally receives opportunities to update his choice of strategy. When such an opportunity arises, the agent selects a strategy that is currently optimal, but only after his payoffs have been randoml ..."
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Cited by 37 (13 self)
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We consider a simple model of stochastic evolution in population games. In our model, each agent occasionally receives opportunities to update his choice of strategy. When such an opportunity arises, the agent selects a strategy that is currently optimal, but only after his payoffs have been
MeanPayoff Games and the MaxAtom Problem
, 2009
"... The maxatom problem asks for the satisfiability of a system of inequality constraints of the type x ≤ max(y, z) + c, where x, y and z are integer variables, and c is an integer constant. We observe that this problem is polynomialtime equivalent to solving meanpayoff games, and therefore at least ..."
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Cited by 1 (0 self)
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The maxatom problem asks for the satisfiability of a system of inequality constraints of the type x ≤ max(y, z) + c, where x, y and z are integer variables, and c is an integer constant. We observe that this problem is polynomialtime equivalent to solving meanpayoff games, and therefore at least
Deterministic priority meanpayoff games as limits of discounted games
, 2006
"... Inspired by the paper of de Alfaro, Henzinger and Majumdar [2] about discounted µcalculus we show new surprising links between parity games and different classes of discounted games. ..."
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Cited by 7 (6 self)
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Inspired by the paper of de Alfaro, Henzinger and Majumdar [2] about discounted µcalculus we show new surprising links between parity games and different classes of discounted games.
Potential theory for mean payoff#11; games
 JOURNAL OF MATHEMATICAL SCIENCES
, 2007
"... We present an O(mn2^n log Z) deterministic algorithm for solving the mean payoff#11; game problem, m and n being respectively the number of arcs and vertices in the game
graph and Z being the maximum weight (we assume that the weights are integer numbers). The theoretical basis for the algorithm is ..."
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Cited by 7 (0 self)
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We present an O(mn2^n log Z) deterministic algorithm for solving the mean payoff#11; game problem, m and n being respectively the number of arcs and vertices in the game
graph and Z being the maximum weight (we assume that the weights are integer numbers). The theoretical basis for the algorithm
A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information
"... Abstract. We consider twoperson zerosum stochastic mean payoff games with perfect information, or BWRgames, given by a digraph G = (V = VB ∪VW ∪VR, E), with local rewards r: E → R, and three types of vertices: black VB, white VW, and random VR. The game is played by two players, White and Black: ..."
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Cited by 11 (6 self)
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to minimize) the limiting mean (that is, average) payoff. It was recently shown in [BEGM09a] that BWRgames are polynomially equivalent with the classical Gillette games, which include many wellknown subclasses, such as cyclic games, simple stochastic games (SSG), stochastic parity games, and Markov decision
Results 1  10
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94