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A DecisionTheoretic Generalization of onLine Learning and an Application to Boosting
, 1996
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A PrimalDual Perspective of Online Learning Algorithms
"... We describe a novel framework for the design and analysis of online learning algorithms based on the notion of duality in constrained optimization. We cast a subfamily of universal online bounds as an optimization problem. Using the weak duality theorem we reduce the process of online learning to ..."
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Cited by 20 (6 self)
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We describe a novel framework for the design and analysis of online learning algorithms based on the notion of duality in constrained optimization. We cast a subfamily of universal online bounds as an optimization problem. Using the weak duality theorem we reduce the process of online learning to the task of incrementally increasing the dual objective function. The amount by which the dual increases serves as a new and natural notion of progress for analyzing online learning algorithms. We are thus able to tie the primal objective value and the number of prediction mistakes using the increase in the dual.
Online learning with imperfect monitoring
 In Proceedings of the 16th Annual Conference on Learning Theory
, 2003
"... Abstract. We study online play of repeated matrix games in which the observations of past actions of the other player and the obtained reward are partial and stochastic. We define the Partial Observation Bayes Envelope (POBE) as the best reward against the worstcase stationary strategy of the oppo ..."
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Cited by 8 (3 self)
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Abstract. We study online play of repeated matrix games in which the observations of past actions of the other player and the obtained reward are partial and stochastic. We define the Partial Observation Bayes Envelope (POBE) as the best reward against the worstcase stationary strategy of the opponent that agrees with past observations. Our goal is to have the (unobserved) average reward above the POBE. For the case where the observations (but not necessarily the rewards) depend on the opponent play alone, an algorithm for attaining the POBE is derived. This algorithm is based on an application of Approachability theory combined with a worstcase view over the unobserved rewards. We also suggest a simplified solution concept for general signaling structure. This concept may fall short of the POBE. 1
Adaptive Strategies and Regret Minimization in arbitrarily varying Markov Environments
 In Proc. of 14th COLT
, 2001
"... We consider the problem of maximizing the average reward in a controlled Markov environment, which also contains some arbitrarily varying elements. This problem is captured by a twoperson stochastic game model involving the reward maximizing agent and a second player, which is free to use an arbitr ..."
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Cited by 5 (0 self)
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We consider the problem of maximizing the average reward in a controlled Markov environment, which also contains some arbitrarily varying elements. This problem is captured by a twoperson stochastic game model involving the reward maximizing agent and a second player, which is free to use an arbitrary (nonstationary and unpredictable) control strategy. While the minimax value of the associated zerosum game provides a guaranteed performance level, the fact that the second player's behavior is observed as the game unfolds opens up the opportunity to improve upon this minimax value if the second player is not playing a worstcase strategy. This basic idea has been formalized in the context of repeated matrix games by the classical notions of regret minimization with respect to the Bayes envelope, where an attainable performance goal is defined in terms of the empirical frequencies of the opponent's actions. This paper presents an extension of these ideas to problems with Markovian dynamics, under appropriate recurrence conditions. The Bayes envelope is first defined in a natural way in terms of the observed state action frequencies. As this envelope may not be attained in general, we define a proper convexification thereof as an attainable solution concept. In the specific case of singlecontroller games, where the opponent alone controls the state transitions, the Bayes envelope itself turns out to be convex and attainable. Some concrete examples are shown to fit in this framework.
On the measure of conflicts: Shapley inconsistency values
 Artificial Intelligence
"... There are relatively few proposals for inconsistency measures for propositional belief bases. However inconsistency measures are potentially as important as information measures for artificial intelligence, and more generally for computer science. In particular, they can be useful to define various ..."
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Cited by 3 (1 self)
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There are relatively few proposals for inconsistency measures for propositional belief bases. However inconsistency measures are potentially as important as information measures for artificial intelligence, and more generally for computer science. In particular, they can be useful to define various operators for belief revision, belief merging, and negotiation. The measures that have been proposed so far can be split into two classes. The first class of measures takes into account the number of formulae required to produce an inconsistency: the more formulae required to produce an inconsistency, the less inconsistent the base. The second class takes into account the proportion of the language that is affected by the inconsistency: the more propositional variables affected, the more inconsistent the base. Both approaches are sensible, but there is no proposal for combining them. We address this need in this paper: our proposal takes into account both the number of variables affected by the inconsistency and the distribution of the inconsistency among the formulae of the base. Our idea is to use existing inconsistency measures in order to define a game in coalitional form, and then to use the Shapley value to obtain an inconsistency measure that indicates the responsibility/contribution of each formula to the overall inconsistency in the base. This allows us to provide a more reliable image of the belief base and of the inconsistency in it. ⇤ This paper is a revised and extended version of the paper ”Shapley Inconcistency Values ” presented at KR’06. 1 1
John von Neumann's work in the theory of games and mathematical economics
 Bulletin of the American Mathematical Society
, 1958
"... Of the many areas of mathematics shaped by his genius, none shows more clearly the influence of John von Neumann than the Theory of Games. This modern approach to problems of competition and cooperation was given a broad foundation in his superlative paper of 1928 [A]. 1 In scope and youthful vigor ..."
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Cited by 2 (0 self)
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Of the many areas of mathematics shaped by his genius, none shows more clearly the influence of John von Neumann than the Theory of Games. This modern approach to problems of competition and cooperation was given a broad foundation in his superlative paper of 1928 [A]. 1 In scope and youthful vigor this work can be compared only to his papers of the same period on the axioms of set theory and the mathematical foundations of quantum mechanics. A decade later, when the Austrian economist Oskar Morgenstern came to Princeton, von Neumann's interest in the theory was reawakened. The result of their active and intensive collaboration during the early years of World War II was the treatise Theory of games and economic behavior [D], in which the basic structure of the 1928 paper is elaborated and extended. Together, the paper and treatise contain a remarkably complete outline of the subject as we know it today, and every writer in the field draws in some measure upon concepts which were there
A note on Kuhn’s theorem
 in Interactive Logic, Proceedings of the 7th Augstus de Morgan Workshop
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A Complete Axiomatization of Differential Game Logic for Hybrid Games
, 2013
"... not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) We introduce differential game logic (dGL) for speci ..."
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Cited by 1 (1 self)
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not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) We introduce differential game logic (dGL) for specifying and verifying properties of hybrid games, i.e. games on hybrid systems combining discrete and continuous dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with different objectives. The logic dGL can be used to study the existence of winning strategies for such hybrid games. We present a simple sound and complete axiomatization of dGL relative to the fixpoint logic of differential equations. We prove hybrid games to be determined and their winning regions to require higher closure ordinals and we identify separating Hybrid systems [Hen96] are dynamical systems combining discrete dynamics and continuous dynamics, which are important, e.g., for modeling how computers control physical systems. Hybrid systems combine difference equations and differential equations with conditional switching, nondeterminism,
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"... reproduced or transmitted in any form or any means without permission in writing from the publisher ..."
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reproduced or transmitted in any form or any means without permission in writing from the publisher