- Abstract: In many applications we seek to optimize 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.
- Keywords: continuous relaxation, discrete stochastic variables, reparameterization trick, variational inference, discrete optimization, stochastic gradient estimation
- TL;DR: We propose simple ways to reduce bias and complexity of stochastic gradient estimators used for learning distributions over discrete variables.