In this paper, we introduce an unbiased gradient simulation algorithms for
solving convex optimization problem with stochastic function compositions. We
show that the unbiased gradient generated from the algorithm has finite
variance and finite expected computation cost. We then combined the unbiased
gradient simulation with two variance reduced algorithms (namely SVRG and SCSG)
and showed that the proposed optimization algorithms based on unbiased gradient
simulations exhibit satisfactory convergence properties. Specifically, in the
SVRG case, the algorithm with simulated gradient can be shown to converge
linearly to optima in expectation and almost surely under strong convexity.
Finally, for the numerical experiment,we applied the algorithms to two
important cases of stochastic function compositions optimization: maximizing
the Cox's partial likelihood model and training conditional random fields.

本文介绍了一种用于解决随机函数组合的凸优化问题的无偏梯度仿真算法，并将其与两个方差减少算法相结合，得出该算法基于无偏梯度仿真展现出令人满意的收敛性能，最后为两个随机函数组合优化问题应用了该算法：最大化 Cox 部分似然模型和训练条件随机场。