Overlapping batches for the assessment of solution quality in stochastic programs

We investigate the use of overlapping batches for assessing solution quality in stochastic programs. Motivated by the original use of overlapping batches in simulation, we present a variant of the multiple replications procedure that reuses data via variably overlapping batches to obtain alternative variance estimators. These estimators have lower variances, where the degree of variance reduction depends on the amount of overlap. We provide several asymptotic properties and present computational results to examine small-sample behavior.