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In this paper, we show that the Away-step Stochastic Frank-Wolfe Algorithm(ASFW) and Pairwise Stochastic Frank-Wolfe algorithm (PSFW) converge linearlyin expectation. We also show that if an algorithm convergences linearly inexpectation then it converges linearly almost surely. In order to prove theseresults, we develop a novel proof technique based on concepts of empiricalprocesses and concentration inequalities. Such a technique has rarely been usedto derive the convergence rates of stochastic optimization algorithms. Inlarge-scale numerical experiments, ASFW and PSFW perform as well as or betterthan their stochastic competitors in actual CPU time.

Linear Convergence of Stochastic Frank Wolfe Variants