Distributed Online Resource Allocation in Open Networks
Yuxuan Liu, Maojiao Ye, Lei Ding, Lihua Xie, Shengyuan Xu · IEEE Transactions on Automatic Control · 2024
This article considers the problem of online resource allocation in an open network where the engaged agents are allowed to join and leave freely. To deal with network openness, each agent possesses two auxiliary variables, utilized to store the sum of gradients and record the number of stored gradients, respectively. Based on the stored information and primal-dual techniques, a distributed online optimization algorithm is constructed for agents to achieve the minimization of their total cost while satisfying local box constraints and a global balancing equality constraint. In the developed algorithm, the agents update their decision variables and dual variables via the projected gradient method and dual averaging method, respectively. A dynamic regret and an accumulation of constraint violation are introduced as performance indices of evaluating the established algorithm. Moreover, if the number of departing agents at each iteration is no larger than the connectivity degree of the communication graph, the upper bounds of both indices are obtained which grow sublinearly under suitable step-sizes, indicating that the proposed algorithm performs well. A simulation case study on economic dispatch in smart grids is given to verify the effectiveness of the developed algorithm.