  Optimizing deep neural networks is one of the main tasks in successful deep
learning. Current state-of-the-art optimizers are adaptive gradient-based
optimization methods such as Adam. Recently, there has been an increasing
interest in formulating gradient-based optimizers in a probabilistic framework
for better estimation of gradients and modeling uncertainties. Here, we propose
to combine both approaches, resulting in the Variational Stochastic Gradient
Descent (VSGD) optimizer. We model gradient updates as a probabilistic model
and utilize stochastic variational inference (SVI) to derive an efficient and
effective update rule. Further, we show how our VSGD method relates to other
adaptive gradient-based optimizers like Adam. Lastly, we carry out experiments
on two image classification datasets and four deep neural network
architectures, where we show that VSGD outperforms Adam and SGD.
