Distributed Online Convex Optimization on Time-Varying Directed Graphs

This paper introduces a class of discrete-time distributed online optimization algorithms, with a group of agents whose communication topology is given by a uniformly strongly connected sequence of time-varying networks. At each time, a private locally Lipschitz strongly convex objective function is revealed to each agent. In the next time step, each agent updates its state using its own objective function and the information gathered from its immediate in-neighbors at that time. Under the assumption that the sequence of communication topologies is uniformly strongly connected, we design an algorithm, distributed over the sequence of time-varying topologies, which guarantees that the individual regret, the difference between the network cost incurred by the agent's states estimation and the cost incurred by the best fixed choice, grows only sublinearly. This algorithm consists of a subgradient flow along with a push-sum step to adjust for the directed nature of the network topologies. We implement the proposed algorithm in a collaborative localization problem, and the results show the proper performance of the algorithm.