Asymptotic properties of dual averaging algorithm for constrained distributed stochastic optimization

Considering the constrained stochastic optimization problem over a time-varying random network, where agents are to collectively minimize sum of objective functions subject common constraint set, we investigate asymptotic properties distributed algorithm based on dual averaging gradients. Different from most existing works algorithms that mainly focused their non-asymptotic properties, prove not only almost sure convergence and rate convergence, but also normality efficiency algorithm. Firstly, for general convex consensus can be achieved estimates converge same optimal point. For case linear optimization, show mirror map averaged sequence identifies active constraints solution with probability 1, which helps us then establish Furthermore, verify is asymptotically optimal. To best our knowledge, it first result algorithms. Finally, numerical example provided justify theoretical analysis.