A Distributed Conjugate Gradient Online Learning Method over Networks

In a distributed online optimization problem with a convex constrained set over an undirected multiagent network, the local objective functions are convex and vary over time. Most of the existing methods used to solve this problem are based on the fastest gradient descent method. However, the convergence speed of these methods is decreased with an increase in the number of iterations. To accelerate the convergence speed of the algorithm, we present a distributed online conjugate gradient algorithm, different from a gradient method, in which the search directions are a set of vectors that are conjugated to each other and the step sizes are obtained through an accurate line search. We analyzed the convergence of the algorithm theoretically and obtained a regret bound of Omml:mfenced close=")" open="(" separators="|"T, where T is the number of iterations. Finally, numerical experiments conducted on a sensor network demonstrate the performance of the proposed algorithm.