Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator
This addresses a key bottleneck in training models with discrete latent variables, offering a more efficient estimator with minimal tuning and computational cost, though it is incremental as it builds on an existing method.
The paper tackled the problem of high variance in gradient estimation for models with discrete latent variables by applying Rao-Blackwellization to the straight-through Gumbel-Softmax estimator, resulting in provably reduced mean squared error and empirically demonstrated variance reduction, faster convergence, and improved performance in two unsupervised latent variable models.
Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple function evaluations, or use learned, input-dependent baselines. Thus, there is a need for estimators that require minimal tuning, are computationally cheap, and have low mean squared error. In this paper, we show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization without increasing the number of function evaluations. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.