Potential-Based Algorithms in On-Line Prediction and Game Theory

  • Authors:
  • Nicolò Cesa-Bianchi;Gábor Lugosi

  • Affiliations:
  • Department of Information Technologies, University of Milan, Via Bramante 65, 26013 Crema, Italy. cesa-bianchi@dti.unimi.it;Department of Economics, Pompeu Fabra University, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain. lugosi@upf.es

  • Venue:
  • Machine Learning
  • Year:
  • 2003

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Abstract

In this paper we show that several known algorithms for sequential prediction problems (including Weighted Majority and the quasi-additive family of Grove, Littlestone, and Schuurmans), 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.