  There is a recent interest on first-order methods for linear programming
(LP). In this paper,we propose a stochastic algorithm using variance reduction
and restarts for solving sharp primal-dual problems such as LP. We show that
the proposed stochastic method exhibits a linear convergence rate for solving
sharp instances with a high probability. In addition, we propose an efficient
coordinate-based stochastic oracle for unconstrained bilinear problems, which
has $\mathcal O(1)$ per iteration cost and improves the complexity of the
existing deterministic and stochastic algorithms. Finally, we show that the
obtained linear convergence rate is nearly optimal (upto $\log$ terms) for a
wide class of stochastic primal dual methods.
