Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients

This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance.