标题： 随机邻近点方法在期望相似性下的单调包含 显示英文标题

标题： Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity

摘要： 单调包含在许多应用中都有广泛的应用，包括最小化、鞍点和平衡问题。 我们引入了新的随机算法，带有或不带有方差减少，以估计可能为集值的单调算子的期望的根，每次迭代仅调用一次随机采样算子的预解算子。 我们还引入了算子之间相似性的概念，即使对于不连续的算子也成立。 我们利用它在强单调的情况下推导出线性收敛结果。 显示英文摘要

摘要： Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of possibly set-valued monotone operators, using at every iteration one call to the resolvent of a randomly sampled operator. We also introduce a notion of similarity between the operators, which holds even for discontinuous operators. We leverage it to derive linear convergence results in the strongly monotone setting.