Learning probability distributions on the weights of neural networks (NNs) has recently proven beneficial in many applications. Bayesian methods, such as Stein variational gradient descent (SVGD), offer an elegant framework to reason about NN model uncertainty. However, by assuming independent Gaussian priors for the individual NN weights (as often applied), SVGD does not impose prior knowledge that there is often structural information (dependence) among weights. We propose efficient posterior learning of structural weight uncertainty, within an SVGD framework, by employing matrix variate Gaussian priors on NN parameters. We further investigate the learned structural uncertainty in sequential decision-making problems, including contextual bandits and reinforcement learning. Experiments on several synthetic and real datasets indicate the superiority of our model, compared with state-of-the-art methods.

本文提出了在SVG框架内通过采用矩阵变量高斯先验对NN参数进行有效的结构权重不确定性后验学习的方法，并进一步研究了顺序决策问题中的学习到的结构不确定性，包括上下文三臂强化学习和强化学习。在几个合成和实际数据集上的实验证明了我们模型相对于最先进的方法的优越性。

序列决策的结构权重不确定性学习