Subgradient-Push Is of the Optimal Convergence Rate

Yixuan Lin; Ji Liu

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arXiv · 2203.16623

Subgradient-Push Is of the Optimal Convergence Rate

Yixuan Lin·Ji Liu

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Abstract

The push-sum based subgradient is an important method for distributed convex optimization over unbalanced directed graphs, which is known to converge at a rate of $O(\ln t/\sqrt{t})$. This paper shows that the subgradient-push algorithm actually converges at a rate of $O(1/\sqrt{t})$, which is the same as that of the single-agent subgradient and thus optimal. The proposed tool for analyzing push-sum based algorithms is of independent interest.

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Yixuan Lin, Ji Liu. 2022-03-30. Subgradient-Push Is of the Optimal Convergence Rate. https://arxiv.org/abs/2203.16623

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