  Mean-field variational inference is one of the most popular approaches to
inference in discrete random fields. Standard mean-field optimization is based
on coordinate descent and in many situations can be impractical. Thus, in
practice, various parallel techniques are used, which either rely on ad-hoc
smoothing with heuristically set parameters, or put strong constraints on the
type of models. In this paper, we propose a novel proximal gradient-based
approach to optimizing the variational objective. It is naturally
parallelizable and easy to implement. We prove its convergence, and then
demonstrate that, in practice, it yields faster convergence and often finds
better optima than more traditional mean-field optimization techniques.
Moreover, our method is less sensitive to the choice of parameters.
