Convergence in distribution of randomized algorithms: the case of partially separable optimization
研究了求解部分块可分优化问题的块随机算法的马尔可夫链性质，刻画了迭代分布的收敛速率和矩行为，并展示了随机化如何恢复算法在部分信息迭代中丢失的良好性质。
Abstract We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators and distributions behind the iterates of stochastic algorithms, and in particular the regularity of Markov operators and rates of convergence of the distributions of the corresponding Markov chains. This provides a detailed characterization of the moments of the sequences beyond just the expected behavior. This also serves as a case study of how randomization restores favorable properties to algorithms that iterations of only partial information destroys. We demonstrate this on stochastic blockwise implementations of the forward–backward and Douglas–Rachford algorithms for nonconvex (and, as a special case, convex), nonsmooth optimization.