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We derive an unbiased estimator for expectations over discrete randomvariables based on sampling without replacement, which reduces variance as itavoids duplicate samples. We show that our estimator can be derived as theRao-Blackwellization of three different estimators. Combining our estimatorwith REINFORCE, we obtain a policy gradient estimator and we reduce itsvariance using a built-in control variate which is obtained without additionalmodel evaluations. The resulting estimator is closely related to other gradientestimators. Experiments with a toy problem, a categorical VariationalAuto-Encoder and a structured prediction problem show that our estimator is theonly estimator that is consistently among the best estimators in both high andlow entropy settings.

Estimating Gradients for Discrete Random Variables by Sampling without Replacement