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We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on(More)
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe Method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating “in-face” directions at each iteration, as well as through new choice rules for selecting(More)
Boosting [6,9,12,15,16] is an extremely successful and popular supervised learning technique that combines multiple “weak” learners into a more powerful “committee.” AdaBoost [7, 12, 16], developed in the context of classification, is one of the earliest and most influential boosting algorithms. In our paper [5], we analyze boosting algorithms in linear(More)
Boosting methods are highly popular and effective supervised learning methods which combine weak learners into a single accurate model with good statistical performance. In this paper, we analyze two well-known boosting methods, AdaBoost and Incremental Forward Stagewise Regression (FSε), by establishing their precise connections to the Mirror Descent(More)
We present several contributions at the interface of first-order methods for convex optimization and problems in statistical machine learning. In the first part of this thesis, we present new results for the Frank-Wolfe method, with a particular focus on: (i) novel computational guarantees that apply for any step-size sequence, (ii) a novel adjustment to(More)
We develop an optimization model and corresponding algorithm for the management of a demand-side platform (DSP), whereby the DSP aims to maximize its own pro€t while acquiring valuable impressions for its advertiser clients. We formulate the problem of pro€t maximization for a DSP interacting with ad exchanges in a real-time bidding environment in a(More)
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