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Potential-Based Algorithms in Online Prediction and Game Theory
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Potential-Based Algorithms in Online Prediction and Game Theory
Nicolò Cesa-Bianchi3 and Gábor Lugosi4 
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Dept. of Information Technologies, University of Milan, Via Bramante 65, 26013 Crema, Italy |
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Department of Economics, Pompeu Fabra University, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain |
Abstract
In this paper we show that several known algorithms for sequential prediction problems (including the quasi-additive family
of Grove et al. and Littlestone and Warmuth’s Weighted Majority), for playing iterated games (including Freund and Schapire’s Hedge and
MW, as well as the Λ-strategies of Hart and Mas-Colell), and for boosting (including AdaBoost) are special cases of a general
decision strategy based on the notion of potential. By analyzing this strategy we derive known performance bounds, as well
as new bounds, as simple corollaries of a single general theorem. Besides offering a new and unified view on a large family
of algorithms, we establish a connection between potential-based analysis in learning and their counterparts independently
developed in game theory. By exploiting this connection, we show that certain learning problems are instances of more general
game-theoretic problems. In particular, we describe a notion of generalized regret and show its applications in learning theory.
Keywords and phrases universal prediction - on-line learning - Blackwell’s strategy - Perceptron algorithm - weighted average predictors - internal regret - boosting
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