Function Space Particle Optimization for Bayesian Neural Networks
This addresses a failure mode in variational inference for over-parameterized Bayesian neural networks, offering improved performance across multiple domains.
The paper tackles the challenge of sub-optimal performance in Bayesian neural network posterior inference by proposing particle optimization in function space instead of parameter space. The method outperforms strong baselines in tasks like prediction, adversarial defense, and reinforcement learning.
While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable variational inference procedures based on the idea of particle optimization have been proposed. These methods directly optimize a set of particles to approximate the target posterior. However, their application to BNNs often yields sub-optimal performance, as such methods have a particular failure mode on over-parameterized models. In this paper, we propose to solve this issue by performing particle optimization directly in the space of regression functions. We demonstrate through extensive experiments that our method successfully overcomes this issue, and outperforms strong baselines in a variety of tasks including prediction, defense against adversarial examples, and reinforcement learning.