Distributed Projected Gradient for Unbalanced Optimization With Delayed Gradient Information

In this paper, a distributed projected gradient algorithm is developed to address a constrained optimization problem encountered in an unbalanced multi-agent network with gradient calculation delay, where each agent cooperates minimizing the global objective function composed of the sum of local strongly convex cost functions subject to a closed and convex constraint set. The proposed algorithm is only based on a row stochastic weight matrix ensuring agents autonomously decide the weighting of information received from their neighbors. Moreover, we design the algorithm with delayed gradient information, which removes the dependence of the current gradient information. We utilize a non-negative decaying step size to analyze the convergence, which shows the algorithm converges at a rate of O(lnT/T). Simulation on a machine learning problem confirms the efficacy of the proposed method.