Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914624963608576 |
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| author | Lu, Haihao Yang, Jinwen |
| author_facet | Lu, Haihao Yang, Jinwen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05530 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming Lu, Haihao Yang, Jinwen Optimization and Control Machine Learning 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. |
| title | Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2111.05530 |