  As a projection-free algorithm, Frank-Wolfe (FW) method, also known as
conditional gradient, has recently received considerable attention in the
machine learning community. In this dissertation, we study several topics on
the FW variants for scalable projection-free optimization.
  We first propose 1-SFW, the first projection-free method that requires only
one sample per iteration to update the optimization variable and yet achieves
the best known complexity bounds for convex, non-convex, and monotone
DR-submodular settings. Then we move forward to the distributed setting, and
develop Quantized Frank-Wolfe (QFW), a general communication-efficient
distributed FW framework for both convex and non-convex objective functions. We
study the performance of QFW in two widely recognized settings: 1) stochastic
optimization and 2) finite-sum optimization. Finally, we propose Black-Box
Continuous Greedy, a derivative-free and projection-free algorithm, that
maximizes a monotone continuous DR-submodular function over a bounded convex
body in Euclidean space.
