A Fourier View of REINFORCE

Adeel Pervez

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arXiv · 1808.03953

A Fourier View of REINFORCE

Adeel Pervez

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Abstract

We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction in gradient estimation for latent variable models: namely, that variance reduction involves eliminating or reducing Fourier coefficients that do not have degree 1. We then use this connection to develop low-variance unbiased gradient estimators for binary latent variable models such as sigmoid belief networks. The estimator is based upon properties of the noise operator from Boolean Fourier theory and involves a sample-dependent baseline added to the REINFORCE estimator in a way that keeps the estimator unbiased. The baseline can be plugged into existing gradient estimators for further variance reduction.

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Adeel Pervez. 2018-08-12. A Fourier View of REINFORCE. https://arxiv.org/abs/1808.03953

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