  We present Quantized Variational Inference, a new algorithm for Evidence
Lower Bound maximization. We show how Optimal Voronoi Tesselation produces
variance free gradients for ELBO optimization at the cost of introducing
asymptotically decaying bias. Subsequently, we propose a Richardson
extrapolation type method to improve the asymptotic bound. We show that using
the Quantized Variational Inference framework leads to fast convergence for
both score function and the reparametrized gradient estimator at a comparable
computational cost. Finally, we propose several experiments to assess the
performance of our method and its limitations.
