Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization

We study stochastic gradient descent for solving conditional optimization problems, in which an objective to be minimized is given by a parametric nested expectation with outer taken respect one random variable and inner the other variable. The of such again expressed as expectation, makes it hard standard Monte Carlo estimator unbiased. In this paper, we show under some conditions that multilevel unbiased has finite variance expected computational cost, so theory from (non-nested) directly applies. also discuss special case yet another cost can constructed.