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We present tools for the analysis of Follow-The-Regularized-Leader (FTRL), Dual Averaging, and Mirror Descent algorithms when the regularizer (equivalently, prox-function or learning rate schedule) is chosen adaptively based on the data.
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On the generalization ability of on-line learning algorithms
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Introductory lectures on convex optimization: a basic course
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Prediction, Learning, and Games
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Adaptive online gradient descent
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Logarithmic regret algorithms for online convex optimization
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Gradient methods for minimizing composite objective function
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Adaptive bound optimization for online convex optimization
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Learnability, stability and uniform convergence
Shai Shalev-Shwartz, Ohad Shamir, Nathan Srebro, and Karthik Sridharan · 2010
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Less regret via online conditioning
Matthew Streeter and H. Brendan McMahan · 2010
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Adaptive subgradient methods for online learning and stochastic optimization
John Duchi, Elad Hazan, and Yoram Singer · 2011
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Follow-the-regularized-leader and mirror descent: Equivalence theorems and L1 regularization
H. Brendan McMahan · 2011
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Contributions to the sequential prediction of arbitrary sequences: applications to the theory of repeated games and empirical studies of the performance of the aggregation of experts
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