Online Learning: Random Averages, Combinatorial Parameters, and Learnability

Part of Advances in Neural Information Processing Systems 23 (NIPS 2010)

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Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari


We develop a theory of online learning by defining several complexity measures. Among them are analogues of Rademacher complexity, covering numbers and fat-shattering dimension from statistical learning theory. Relationship among these complexity measures, their connection to online learning, and tools for bounding them are provided. We apply these results to various learning problems. We provide a complete characterization of online learnability in the supervised setting.