Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming

10 Nov 2021  ·  Haihao Lu, Jinwen Yang ·

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.

PDF Abstract
No code implementations yet. Submit your code now



  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here