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- Elad Hazan, Adam Tauman Kalai, Satyen Kale, Amit Agarwal
- Machine Learning
- 2006

In an online convex optimization problem a decision-maker makes a sequence of decisions, i.e., chooses a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters a sequence of (possibly unrelated) convex cost functions. Zinkevich (ICML 2003) introduced this framework, which models many natural repeated… (More)

- Sanjeev Arora, Elad Hazan, Satyen Kale
- Theory of Computing
- 2012

Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simple… (More)

The contingency table is a work horse of official statistics, the format of reported data for the US Census, Bureau of Labor Statistics, and the Internal Revenue Service. In many settings such as these privacy is not only ethically mandated, but frequently legally as well. Consequently there is an extensive and diverse literature dedicated to the problems… (More)

- Elad Hazan, Satyen Kale
- COLT
- 2011

We give a novel algorithm for stochastic strongly-convex optimization in the gradient oracle model which returns an O( 1 T )-approximate solution after T gradient updates. This rate of convergence is optimal in the gradient oracle model. This improves upon the previously known best rate of O( log(T ) T ), which was obtained by applying an online… (More)

- Sanjeev Arora, Satyen Kale
- J. ACM
- 2007

Semidefinite programs (SDPs) have been used in many recent approximation algorithms. We develop a general primal-dual approach to solve SDPs using a generalization of the well-known multiplicative weights update rule to symmetric matrices. For a number of problems, such as S<scp>parsest</scp> C<scp>ut</scp> and B<scp>alanced</scp> S<scp>eparator</scp> in… (More)

- Amit Agarwal, Elad Hazan, Satyen Kale, Robert E. Schapire
- ICML
- 2006

We experimentally study on-line investment algorithms first proposed by Agarwal and Hazan and extended by Hazan et al. which achieve almost the same wealth as the best constant-rebalanced portfolio determined in hindsight. These algorithms are the first to combine optimal logarithmic regret bounds with efficient deterministic computability. They are based… (More)

We present a new algorithm for the contextual bandit learning problem, where the learner repeatedly takes one of K actions in response to the observed context, and observes the reward only for that action. Our method assumes access to an oracle for solving fully supervised costsensitive classification problems and achieves the statistically optimal regret… (More)

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and parallelizable dense linear algebra… (More)

- Sanjeev Arora, Elad Hazan, Satyen Kale
- APPROX-RANDOM
- 2006

We describe a simple random-sampling based procedure for producing sparse matrix approximations. Our procedure and analysis are extremely simple: the analysis uses nothing more than the Chernoff-Hoeffding bounds. Despite the simplicity, the approximation is comparable and sometimes better than previous work. Our algorithm computes the sparse matrix… (More)

- Arpita Ghosh, Satyen Kale, R. Preston McAfee
- EC
- 2011

A large fraction of user-generated content on the Web, such as posts or comments on popular online forums, consists of abuse or spam. Due to the volume of contributions on popular sites, a few trusted moderators cannot identify all such abusive content, so viewer ratings of contributions must be used for moderation. But not all viewers who rate content are… (More)