On the Performance of Direct Loss Minimization for Bayesian Neural Networks

TL;DR

This paper evaluates the effectiveness of Direct Loss Minimization (DLM) for Bayesian neural networks, revealing its limitations and contrasting it with traditional ELBO optimization.

Contribution

The study provides a detailed analysis of DLM's performance on BNNs, explaining why it underperforms compared to ELBO-based methods.

Findings

DLM does not outperform ELBO in Bayesian neural networks

The paper uncovers reasons for DLM's failure in BNNs

Insights into the relationship between DLM and ELBO optimization

Abstract

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.