Direct Optimization through $\arg \max$ for Discrete Variational Auto-Encoder
This addresses a bottleneck in training discrete latent variable models for researchers in machine learning, though it appears incremental as it builds on existing direct loss minimization techniques.
The paper tackles the non-differentiability issue in discrete variational auto-encoders by proposing direct optimization through arg max, avoiding softmax relaxations, and demonstrates effectiveness in models with unstructured and structured discrete latent variables.
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.