Rao-Blackwellized Stochastic Gradients for Discrete Distributions

10/10/2018

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by   Runjing Liu, et al.

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We wish to compute the gradient of an expectation over a finite or countably infinite sample space having K ≤∞ categories. When K is indeed infinite, or finite but very large, the relevant summation is intractable. Accordingly, various stochastic gradient estimators have been proposed. In this paper, we describe a technique that can be applied to reduce the variance of any such estimator, without changing its bias---in particular, unbiasedness is retained. We show that our technique is an instance of Rao-Blackwellization, and we demonstrate the improvement it yields in empirical studies on both synthetic and real-world data.