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Evaluating the Variance of Likelihood-Ratio Gradient Estimators
Seiya Tokui · Issei Sato

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #33

The likelihood-ratio method is often used to estimate gradients of stochastic computations, for which baselines are required to reduce the estimation variance. Many types of baselines have been proposed, although their degree of optimality is not well understood. In this study, we establish a novel framework of gradient estimation that includes most of the common gradient estimators as special cases. The framework gives a natural derivation of the optimal estimator that can be interpreted as a special case of the likelihood-ratio method so that we can evaluate the optimal degree of practical techniques with it. It bridges the likelihood-ratio method and the reparameterization trick while still supporting discrete variables. It is derived from the exchange property of the differentiation and integration. To be more specific, it is derived by the reparameterization trick and local marginalization analogous to the local expectation gradient. We evaluate various baselines and the optimal estimator for variational learning and show that the performance of the modern estimators is close to the optimal estimator.

Author Information

Seiya Tokui (Preferred Networks / The University of Tokyo)

Seiya Tokui is a researcher at Preferred Networks, Inc., Japan, and also a Ph.D. student at the University of Tokyo. He received the master’s degree in mathematical informatics at the University of Tokyo in 2012. He is the lead developer of the deep learning framework, Chainer. His current research interests include deep learning, its software design, computer vision, and natural language processing.

Issei Sato (University of Tokyo / RIKEN)

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