Distributed subgradient-push online convex optimization on time-varying directed graphs

Abstract

This paper presents a class of subgradient-push algorithms for online distributed optimization over time-varying networks. In this setting, a private strongly convex objective function is revealed to each agent at each time step. In the next time step, this agent makes a decision about its state using this knowledge, along with the information gathered only from its neighboring agents, prescribed by a sequence of time-varying directed graphs. Under the assumption that this sequence is uniformly strongly connected, we design an algorithm, distributed over this time-varying topology, that guarantees that the individual regret, the difference between the accumulated cost of agents' states and the best static offline cost, grows only sublinearly. Simulations illustrate our results.