  We propose a novel adaptive, accelerated algorithm for the stochastic
constrained convex optimization setting. Our method, which is inspired by the
Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for
smooth/non-smooth problems with either deterministic/stochastic first-order
oracles. This is done without any prior knowledge of the smoothness nor the
noise properties of the problem. To the best of our knowledge, this is the
first adaptive, unified algorithm that achieves the optimal rates in the
constrained setting. We demonstrate the practical performance of our framework
through extensive numerical experiments.
