Skip to yearly menu bar Skip to main content


Blended Conditonal Gradients

Gábor Braun · Sebastian Pokutta · Dan Tu · Stephen Wright

Pacific Ballroom #191

Keywords: [ Supervised Learning ] [ Sparsity and Compressed Sensing ] [ Large Scale Learning and Big Data ] [ Convex Optimization ]


We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank–Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and pairwise steps, but still achieving linear convergence for strongly convex functions, along with good practical performance. Our approach retains all favorable properties of conditional gradient algorithms, notably avoidance of projections onto P and maintenance of iterates as sparse convex combinations of a limited number of extreme points of P. The algorithm is lazy, making use of inexpensive inexact solutions of the linear programming subproblem that characterizes the conditional gradient approach. It decreases measures of optimality (primal and dual gaps) rapidly, both in the number of iterations and in wall-clock time, outperforming even the lazy conditional gradient algorithms of Braun et al. 2017. We also present a streamlined version of the algorithm that applies when P is the probability simplex.

Live content is unavailable. Log in and register to view live content