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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. Zinke-vich [Zin03] introduced this framework, which models many natural repeated(More)
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)
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 strongly-convex(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)
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)
Prediction from expert advice is a fundamental problem in machine learning. A major pillar of the field is the existence of learning algorithms whose average loss approaches that of the best expert in hindsight (in other words, whose average regret approaches zero). Traditionally the regret of online algorithms was bounded in terms of the number of(More)
We address the problem of learning in an on-line setting where the learner repeatedly observes features, selects among a set of actions, and receives reward for the action taken. We provide the first efficient algorithm with an optimal regret. Our algorithm uses a cost sensitive classification learner as an oracle and has a running time polylog(N), where N(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 cost-sensitive classification problems and achieves the statistically optimal regret(More)
The computational bottleneck in applying online learning to massive data sets is usually the projection step. We present efficient on-line learning algorithms that eschew projections in favor of much more efficient linear optimization steps using the Frank-Wolfe technique. We obtain a range of regret bounds for online convex optimization, with better bounds(More)
Semidefinite programming (SDP) relaxations appear in many recent approximation algorithms but the only general technique for solving such SDP relaxations is via interior point methods. We use a Lagrangian-relaxation based technique (modified from the papers of Plotkin, Shmoys, and Tardos (PST), and Klein and Lu) to derive faster algorithms for approximately(More)