  We consider the problem of minimizing the sum of two convex functions. One of
those functions has Lipschitz-continuous gradients, and can be accessed via
stochastic oracles, whereas the other is "simple". We provide a Bregman-type
algorithm with accelerated convergence in function values to a ball containing
the minimum. The radius of this ball depends on problem-dependent constants,
including the variance of the stochastic oracle. We further show that this
algorithmic setup naturally leads to a variant of Frank-Wolfe achieving
acceleration under parallelization. More precisely, when minimizing a smooth
convex function on a bounded domain, we show that one can achieve an $\epsilon$
primal-dual gap (in expectation) in $\tilde{O}(1/ \sqrt{\epsilon})$ iterations,
by only accessing gradients of the original function and a linear maximization
oracle with $O(1/\sqrt{\epsilon})$ computing units in parallel. We illustrate
this fast convergence on synthetic numerical experiments.
