  Traditional algorithms for stochastic optimization require projecting the
solution at each iteration into a given domain to ensure its feasibility. When
facing complex domains, such as positive semi-definite cones, the projection
operation can be expensive, leading to a high computational cost per iteration.
In this paper, we present a novel algorithm that aims to reduce the number of
projections for stochastic optimization. The proposed algorithm combines the
strength of several recent developments in stochastic optimization, including
mini-batch, extra-gradient, and epoch gradient descent, in order to effectively
explore the smoothness and strong convexity. We show, both in expectation and
with a high probability, that when the objective function is both smooth and
strongly convex, the proposed algorithm achieves the optimal $O(1/T)$ rate of
convergence with only $O(\log T)$ projections. Our empirical study verifies the
theoretical result.
