Statistics Papers

Document Type

Conference Paper

Date of this Version

2011

Publication Source

JMLR: Workshop and Conference Proceedings

Volume

19

Start Page

559

Last Page

594

Abstract

We study online learnability of a wide class of problems, extending the results of Rakhlin et al. (2010a) to general notions of performance measure well beyond external regret. Our framework simultaneously captures such well-known notions as internal and general Φ-regret, learning with non-additive global cost functions, Blackwell's approachability, calibration of forecasters, and more. We show that learnability in all these situations is due to control of the same three quantities: a martingale convergence term, a term describing the ability to perform well if future is known, and a generalization of sequential Rademacher complexity, studied in Rakhlin et al. (2010a). Since we directly study complexity of the problem instead of focusing on efficient algorithms, we are able to improve and extend many known results which have been previously derived via an algorithmic construction.

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Date Posted: 27 November 2017

This document has been peer reviewed.