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.
Recommended Citation
Rakhlin, A., Sridharan, K., & Tewari, A. (2011). Online Learning: Beyond Regret. JMLR: Workshop and Conference Proceedings, 19 559-594. Retrieved from https://repository.upenn.edu/statistics_papers/133
Date Posted: 27 November 2017
This document has been peer reviewed.