Direct optimization through arg max for discrete variational auto-encoder

Abstract

Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an arg max operation and is non-differentiable. In contrast to previous works which resort to softmax-based relaxations, we propose to optimize it directly by applying the direct loss minimization approach. Our proposal extends naturally to structured discrete latent variable models when evaluating the arg max operation is tractable. We demonstrate empirically the effectiveness of the direct loss minimization technique in variational autoencoders with both unstructured and structured discrete latent variables.