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Optimal strategies and minimax lower bounds for online convex games

Abernethy, Jacob D., Bartlett, Peter L., Rakhlin, Alexander, & Tewari, Ambuj (2008) Optimal strategies and minimax lower bounds for online convex games. Technical Report, UCB/EECS-2008-19. University of California, Berkeley, Berkeley, California (USA).

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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.

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ID Code: 44006
Item Type: Report
Additional Information: Fulltext freely available see link above
Additional URLs:
Keywords: OAVJ
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > INFORMATION SYSTEMS (080600)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright © 2008, by the author(s). All rights reserved.
Copyright Statement: Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission.
Deposited On: 18 Aug 2011 08:21
Last Modified: 18 Aug 2014 12:07

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