Review for NeurIPS paper: Decision-Making with Auto-Encoding Variational Bayes

The proposed approach is to 1) train the generative model and inference network using the - variational auto-encoder ELBO (VAE), - importance weighted auto-encoder (IWAE), - reweighted wake-sleep with the wake-step for training the inference network (RWS), and the - chi-squared objective (X-VAE), objectives and pick one that has the maximum evidence, estimated by the IWAE objective with a lot of particles.