Open AccessProceedings Article
Adaptive Online Gradient Descent
Elad Hazan,Alexander Rakhlin,Peter L. Bartlett +2 more
- Vol. 20, pp 65-72
TLDR
An algorithm is provided, 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 √T and log T and shows strong optimality of the algorithm.Abstract:
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 √T and log T. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.read more
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References
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Book
Prediction, learning, and games
Nicolò Cesa-Bianchi,Gábor Lugosi +1 more
TL;DR: In this paper, the authors provide a comprehensive treatment of the problem of predicting individual sequences using expert advice, a general framework within which many related problems can be cast and discussed, such as repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems.
Proceedings Article
Online convex programming and generalized infinitesimal gradient ascent
TL;DR: An algorithm for convex programming is introduced, and it is shown that it is really a generalization of infinitesimal gradient ascent, and the results here imply that generalized inf initesimalgradient ascent (GIGA) is universally consistent.
Journal ArticleDOI
Logarithmic regret algorithms for online convex optimization
TL;DR: Several algorithms achieving logarithmic regret are proposed, which besides being more general are also much more efficient to implement, and give rise to an efficient algorithm based on the Newton method for optimization, a new tool in the field.
Book ChapterDOI
Logarithmic regret algorithms for online convex optimization
TL;DR: This paper proposes several algorithms achieving logarithmic regret, which besides being more general are also much more efficient to implement, and gives an efficient algorithm based on the Newton method for optimization, a new tool in the field.
Proceedings Article
Convex Repeated Games and Fenchel Duality
Shai Shalev-Shwartz,Yoram Singer +1 more
TL;DR: It is shown that various online learning and boosting algorithms can be all derived as special cases of the algorithmic framework described, which stems from a connection that is built between the notions of regret in game theory and weak duality in convex optimization.