Abstract

A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal.

Keywords

RegretMinimaxRegular polygonMathematical optimizationMathematicsPerspective (graphical)Convex setSet (abstract data type)Function (biology)Convex hullConvex functionConvex analysisConvex optimizationCombinatoricsComputer scienceArtificial intelligence

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Publication Info

Year
2008
Type
article
Citations
102
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Jacob Abernethy, Peter L. Bartlett, Alexander Rakhlin et al. (2008). Optimal Strategies and Minimax Lower Bounds for Online Convex Games. ScholarlyCommons (University of Pennsylvania) .