Paul Grigas

New analysis and results for the Frank---Wolfe method

We present new results for the Frank–Wolfe method (also known as the conditional gradient 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 the warm-start quality of the initial (and subsequent) iterates. Our results include computational guarantees for both duality/bound gaps and the so-called FW gaps. Lastly, we present complexity bounds in the presence of approximate computation of gradients and/or linear optimization subproblem solutions.

A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives

In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS

Profit Maximization for Online Advertising Demand-Side Platforms

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New Analysis and Results for the Conditional Gradient Method

) and least squares boosting (LS-Boost(

An Extended Frank--Wolfe Method with “In-Face” Directions, and Its Application to Low-Rank Matrix Completion

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Smart "Predict, then Optimize".

)), can be viewed as subgradient descent to minimize the loss function defined as the maximum absolute correlation between the features and residuals. We also propose a modification of FS

AdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods

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Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods

that yields an algorithm for the Lasso, and that may be easily extended to an algorithm that computes the Lasso path for different values of the regularization parameter. Furthermore, we show that these new algorithms for the Lasso may also be interpreted as the same master algorithm (subgradient descent), applied to a regularized version of the maximum absolute correlation loss function. We derive novel, comprehensive computational guarantees for several boosting algorithms in linear regression (including LS-Boost(

Optimal Bidding, Allocation and Budget Spending for a Demand Side Platform Under Many Auction Types

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New analysis and results for the Frank–Wolfe method

) and FS