  Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method
motivated as regularized loss minimization. Compared to variational inference,
it replaces the loss term in the evidence lower bound (ELBO) with the
predictive log loss, which is the same loss function used in evaluation. A
number of theoretical and empirical results in prior work suggest that DLM can
significantly improve over ELBO optimization for some models. However, as we
point out in this paper, this is not the case for Bayesian neural networks
(BNNs). The paper explores the practical performance of DLM for BNN, the
reasons for its failure and its relationship to optimizing the ELBO, uncovering
some interesting facts about both algorithms.
