We develop a novel algorithm that draws samples according to the current allocation estimate, refines variance estimates and consequent allocation estimates based on these samples, and then iterates until a convergence criterion is satisfied. This algorithm is “online” in the machine learning sense that the feedback it has received so far via the label judgments influences the next set of samples that are drawn. Our algorithm exploits this feedback to draw a total number of samples that are near-optimal given a chosen stratification strategy