Improved Gradient-Based Optimization Over Discrete Distributions

Evgeny Andriyash; Arash Vahdat; Bill Macready

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arXiv · 1810.00116

Improved Gradient-Based Optimization Over Discrete Distributions

Evgeny Andriyash·Arash Vahdat·Bill Macready

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Abstract

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks.

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BibTeX RIS

Evgeny Andriyash, Arash Vahdat, Bill Macready. 2018-09-29. Improved Gradient-Based Optimization Over Discrete Distributions. https://arxiv.org/abs/1810.00116

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