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SCHAPIRE: Adaptive game playing using multiplicative weights
 Games and Economic Behavior
, 1999
"... We present a simple algorithm for playing a repeated game. We show that a player using this algorithm suffers average loss that is guaranteed to come close to the minimum loss achievable by any fixed strategy. Our bounds are nonasymptotic and hold for any opponent. The algorithm, which uses the mult ..."
Abstract

Cited by 134 (14 self)
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We present a simple algorithm for playing a repeated game. We show that a player using this algorithm suffers average loss that is guaranteed to come close to the minimum loss achievable by any fixed strategy. Our bounds are nonasymptotic and hold for any opponent. The algorithm, which uses the multiplicativeweight methods of Littlestone and Warmuth, is analyzed using the Kullback–Liebler divergence. This analysis yields a new, simple proof of the min–max theorem, as well as a provable method of approximately solving a game. A variant of our gameplaying algorithm is proved to be optimal in a very strong sense. Journal of Economic Literature
Game Theory, Online Prediction and Boosting
 In Proceedings of the Ninth Annual Conference on Computational Learning Theory
, 1996
"... We study the close connections between game theory, online prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the online prediction methods of Littlestone and Warmuth. The analysis of this algorithm yields a simple pr ..."
Abstract

Cited by 133 (13 self)
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We study the close connections between game theory, online prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the online prediction methods of Littlestone and Warmuth. The analysis of this algorithm yields a simple proof of von Neumann's famous minmax theorem, as well as a provable method of approximately solving a game. We then show that the online prediction model is obtained by applying this gameplaying algorithm to an appropriate choice of game and that boosting is obtained by applying the same algorithm to the "dual" of this game. 1 INTRODUCTION The purpose of this paper is to bring out the close connections between game theory, online prediction and boosting. Briefly, game theory is the study of games and other interactions of various sorts. Online prediction is a learning model in which an agent predicts the classification of a sequence of items and attempts to minimize the total number of pre...
Proceedings of the Ninth Annual Conference on Computational Learning Theory, 1996. Game Theory, Online Prediction and Boosting
"... We study the close connections between game theory, online prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the online prediction methods of Littlestone and Warmuth. The analysis of this algorithm yields a simple pr ..."
Abstract
 Add to MetaCart
We study the close connections between game theory, online prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the online prediction methods of Littlestone and Warmuth. The analysis of this algorithm yields a simple proof of von Neumann’s famous minmax theorem, as well as a provable method of approximately solving a game. We then show that the online prediction model is obtained by applying this gameplaying algorithm to an appropriate choice of game and that boosting is obtained by applying the same algorithm to the “dual ” of this game. 1