Asynchronous parallel stochastic optimization for non-convex problems becomes more and more important in machine learning especially due to the popularity of deep learning. The Frank-Wolfe (a.k.a. conditional gradient) algorithms has regained much interest because of its projection-free property and the ability of handling structured constraints. However, our understanding of asynchronous stochastic Frank-Wolfe algorithms is extremely limited especially in the non-convex setting. To address this challenging problem, in this paper, we propose our asynchronous stochastic Frank-Wolfe algorithm (AsySFW) and its variance reduction version (AsySVFW) for solving the constrained non-convex optimization problems. More importantly, we prove the fast convergence rates of AsySFW and AsySVFW in the non-convex setting. To the best of our knowledge, AsySFW and AsySVFW are the first asynchronous parallel stochastic algorithms with convergence guarantees for solving the constrained non-convex optimization problems. The experimental results on real high-dimensional gray-scale images not only confirm the fast convergence of our algorithms, but also show a near-linear speedup on a parallel system with shared memory due to the lock-free implementation.
Posterior concentration and fast convergence rates for generalized Bayesian learning
