Convergence analysis of the stochastic reflected forward–backward splitting algorithm

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