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arXiv · 2102.08906

Convergence analysis of the stochastic reflected forward-backward splitting algorithm

Nguyen Van Dung·Bang Cong Vu
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Abstract

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate $\mathcal{O}(log(n)/n)$ in expectation for the strongly monotone case, as well as almost sure convergence for the general case. Furthermore, in the context of application to convex-concave saddle point problems, we derive the rate of the primal-dual gap. In particular, we also obtain $\mathcal{O}(1/n)$ rate convergence of the primal-dual gap in the deterministic setting.

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Nguyen Van Dung, Bang Cong Vu. 2021-02-17. Convergence analysis of the stochastic reflected forward-backward splitting algorithm. https://arxiv.org/abs/2102.08906

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