Online Distributed Newton Step Algorithm for Multi-agent Optimization Over General Unbalanced Networks

This paper studies distributed online optimization over multi-agent networks. Agents work together to optimize the global loss function, which can be expressed as the sum of the local loss functions of all agents. All local loss functions change with time, and information about the loss function can only be obtained after the agent has made a decision. For such a scenario, the performance of many current algorithms will be challenged if the communication topology is unbalanced because, in this case, the contribution share of each agent in the optimization process is not equal to its share in the total loss function. We designed a distributed online Newton step algorithm in unbalanced networks, which add an additional auxiliary variable to scale the share of each agent's contribution in the algorithm. The algorithm uses only row-stochastic matrix instead of double stochastic matrix, and guarantees the logarithmic convergence of regret for α-exp concave loss functions. Simulation results show the effectiveness of the proposed algorithm in unbalanced topology.