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- Jacob D. Abernethy, Elad Hazan, Alexander Rakhlin
- COLT
- 2008

We introduce an efficient algorithm for the problem of online linear optimization in the bandit setting which achieves the optimal O*(âˆšT)regret. The setting is a natural generalization of theâ€¦ (More)

- Alexander Rakhlin, Ohad Shamir, Karthik Sridharan
- ICML
- 2012

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate wasâ€¦ (More)

- Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari
- NIPS
- 2010

We develop a theory of online learning by defining several complexity measures. Among them are analogues of Rademacher complexity, covering numbers and fatshattering dimension from statisticalâ€¦ (More)

- Alexander Rakhlin, Karthik Sridharan
- COLT
- 2013

We present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences. Specifically if the sequence encountered by the learner is described well by aâ€¦ (More)

- Alexander Rakhlin, Karthik Sridharan
- NIPS
- 2013

We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offlineâ€¦ (More)

First, we demonstrate how the Contraction Lemma for Rademacher averages can be used to obtain tight performance guarantees for learning methods [3]. In particular, we derive risk bounds for a greedyâ€¦ (More)

We establish necessary and sufficient conditions for a uniform martingale Law of Large Numbers. We extend the technique of symmetrization to the case of dependent random variables and provideâ€¦ (More)

- Alexander Rakhlin, Ohad Shamir, Karthik Sridharan
- NIPS
- 2012

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yieldâ€¦ (More)

- Maxim Raginsky, Alexander Rakhlin, Matus Telgarsky
- COLT
- 2017

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient atâ€¦ (More)

This paper addresses the problem of minimizing a convex, Lipschitz function f over a convex, compact set X under a stochastic bandit feedback model. In this model, the algorithm is allowed to observeâ€¦ (More)