Mean-field variational inference (VI) iscomputationally scalable, but its highlydemanding independence requirement hinders it from being applied to wider scenarios. Although many VI methods that take correlation into account have been proposed, these methods generally are not scalable enough to capture the correlation among data instances, which often arises in applications involving graphs or explicit constraints among instances.

In the paper, we propose a class of efficient mirror descent ascent methods to solve the nonsmooth nonconvex-strongly-concave minimax problems by using dynamic mirror functions, and introduce a convergence analysis framework to conduct rigorous theoretical analysis forourmirror descent ascent methods. For our stochastic algorithms, we first prove that the mini-batch stochastic mirror descent ascent (SMDA) method obtains agradient complexity ofO(κ3 4)for findingan -stationary point,whereκdenotes thecondition number.

The seeder generates as diversified candidate solutions as possible (seeds) while being dedicated to exploring over the full combinatorial action space (i.e.,sequence ofassignment action).