Distributed Mirror Descent with Integral Feedback: Convergence Analysis from a Dynamical System Perspective

This work addresses distributed risk minimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. An integral feedback is incorporated into the update, allowing the algorithm to converge with a constant step-size (when discretized). We establish the asymptotic convergence of the algorithm using Lyapunov stability analysis and also prove that the algorithm indeed achieves (local) exponential convergence. We provide a numerical experiment on a real data-set as a validation of the convergence speed of our algorithm.