We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan (et al.) eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan (et al.) for strongly convex functions, achieving intermediate rates between sqrtT and log T. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.
Title
Adaptive Online Gradient Descent
Published
2007-06-14
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2007-82
Type
Text
Extent
14 p
Archive
The Engineering Library
Usage Statement
Researchers may make free and open use of the UC Berkeley Library’s digitized public domain materials. However, some materials in our online collections may be protected by U.S. copyright law (Title 17, U.S.C.). Use or reproduction of materials protected by copyright beyond that allowed by fair use (Title 17, U.S.C. § 107) requires permission from the copyright owners. The use or reproduction of some materials may also be restricted by terms of University of California gift or purchase agreements, privacy and publicity rights, or trademark law. Responsibility for determining rights status and permissibility of any use or reproduction rests exclusively with the researcher. To learn more or make inquiries, please see our permissions policies (https://www.lib.berkeley.edu/about/permissions-policies).
