On the iteration complexity analysis of Stochastic Primal-Dual Hybrid Gradient approach with high probability

Our new approach overcomes these issues by exploring the special structure of the regularization term and sampling a few data points at each iteration. Rather than analyzing the convergence in expectation, we provide the detailed iteration complexity analysis for the cases of both uniformly and non-uniformly averaged iterates with high probability. This strongly supports the good practical performance of the proposed approach. Numerical experiments demonstrate that the efficiency of stochastic PDHG, which outperforms other competing algorithms, as expected by the high-probability convergence analysis.