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13
Online learning with predictable sequences
 In COLT
, 2013
"... We present methods for online linear optimization that take advantage of benign (as opposed to worstcase) sequences. Specifically if the sequence encountered by the learner is described well by a known “predictable process”, the algorithms presented enjoy tighter bounds as compared to the typical w ..."
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We present methods for online linear optimization that take advantage of benign (as opposed to worstcase) sequences. Specifically if the sequence encountered by the learner is described well by a known “predictable process”, the algorithms presented enjoy tighter bounds as compared to the typical worst case bounds. Additionally, the methods achieve the usual worstcase regret bounds if the sequence is not benign. Our approach can be seen as a way of adding prior knowledge about the sequence within the paradigm of online learning. The setting is shown to encompass partial and side information. Variance and pathlength bounds [11, 9] can be seen as particular examples of online learning with simple predictable sequences. We further extend our methods and results to include competing with a set of possible predictable processes (models), that is “learning ” the predictable process itself concurrently with using it to obtain better regret guarantees. We show that such model selection is possible under various assumptions on the available feedback. Our results suggest a promising direction of further research with potential applications to stock market and time series prediction. 1
A Secondorder Bound with Excess Losses
"... We study online aggregation of the predictions of experts, and first show new secondorder regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are ..."
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We study online aggregation of the predictions of experts, and first show new secondorder regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess losses, the differences between the instantaneous losses suffered by the algorithm and the ones of a given expert. We then demonstrate the interest of these bounds in the context of experts that report their confidences as a number in the interval [0, 1] using a generic reduction to the standard setting. We conclude by two other applications in the standard setting, which improve the known bounds in case of small excess losses and show a bounded regret against i.i.d. sequences of losses. 1.
Commentary on “Online Optimization with Gradual Variations”
"... This commentary is about (Chiang et al., 2012b). This paper is the result of a merge ..."
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This commentary is about (Chiang et al., 2012b). This paper is the result of a merge
convex
"... Noname manuscript No. (will be inserted by the editor) Regret bounded by gradual variation for online ..."
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Noname manuscript No. (will be inserted by the editor) Regret bounded by gradual variation for online
JMLR: Workshop and Conference Proceedings vol 30 (2013) 1–21 Regret Minimization for Branching Experts
"... We study regret minimization bounds in which the dependence on the number of experts is replaced by measures of the realized complexity of the expert class. The measures we consider are defined in retrospect given the realized losses. We concentrate on two interesting cases. In the first, our measur ..."
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We study regret minimization bounds in which the dependence on the number of experts is replaced by measures of the realized complexity of the expert class. The measures we consider are defined in retrospect given the realized losses. We concentrate on two interesting cases. In the first, our measure of complexity is the number of different “leading experts”, namely, experts that were best at some point in time. We derive regret bounds that depend only on this measure, independent of the total number of experts. We also consider a case where all experts remain grouped in just a few clusters in terms of their realized cumulative losses. Here too, our regret bounds depend only on the number of clusters determined in retrospect, which serves as a measure of complexity. Our results are obtained as special cases of a more general analysis for a setting of branching experts, where the set of experts may grow over time according to a treelike structure, determined by an adversary. For this setting of branching experts, we give algorithms and analysis that cover both the full information and the bandit scenarios.
PREDICTABLE SEQUENCES AND COMPETING WITH STRATEGIES
"... It seems like yesterday that I arrived on the beautiful campus of the University of Pennsylvania, and it is hard to believe that four wonderful years have already passed. With memories everywhere across the campus, I owe thanks to many people in many ways. I would like to express my deepest apprecia ..."
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It seems like yesterday that I arrived on the beautiful campus of the University of Pennsylvania, and it is hard to believe that four wonderful years have already passed. With memories everywhere across the campus, I owe thanks to many people in many ways. I would like to express my deepest appreciation to all of my wonderful professors. Thanks to Professor Charles L. Epstein for accepting me to The Graduate Group in Applied Mathematics and Computational Science (AMCS). That marked the beginning of all the memories. Thanks also to Professor Abraham J. Wyner for introducing me to the field of statistics and to the Wharton Statistics Department and many interesting projects. I would also like to extend my appreciation to Professor Alexander Rakhlin for introducing me to the field of online learning, and for his support and encouragement throughout my research. Karthik Sridharan offered many brilliant and inspiring ideas, and contributed greatly to my research. Professor Dean Foster served on my thesis committee, and provided extremely valuable career advice. Many thanks, as well, to all of the great professors who instructed me during my twenty courses at Penn. I could not have completed this program without the generous financial support of several professors and departments at the University of Pennsylvania. Thanks
Adaptivity and Optimism: An Improved Exponentiated Gradient Algorithm
"... We present an adaptive variant of the exponentiated gradient algorithm. Leveraging the optimistic learning framework of Rakhlin & Sridharan (2012), we obtain regret bounds that in the learning from experts setting depend on the variance and path length of the best expert, improving on resul ..."
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We present an adaptive variant of the exponentiated gradient algorithm. Leveraging the optimistic learning framework of Rakhlin & Sridharan (2012), we obtain regret bounds that in the learning from experts setting depend on the variance and path length of the best expert, improving on results by Hazan & Kale (2008) and Chiang et al. (2012), and resolving an open problem posed by Kale (2012). Our techniques naturally extend to matrixvalued loss functions, where we present an adaptive matrix exponentiated gradient algorithm. To obtain the optimal regret bound in the matrix case, we generalize the FollowtheRegularizedLeader algorithm to vectorvalued payoffs, which may be of independent interest. 1.