Distributed Online Constrained Optimization With Feedback Delays

We investigate multiagent distributed online constrained convex optimization problems with feedback delays, where agents make sequential decisions before being aware of the cost and constraint functions. The main purpose of the distributed online constrained convex optimization problem is to cooperatively minimize the sum of time-varying local cost functions subject to time-varying coupled inequality constraints. The feedback information of the distributed online optimization problem is revealed to agents with time delays, which is common in practice. Every node in the system can interact with neighbors through a time-varying sequence of directed communication topologies, which is uniformly strongly connected. The distributed online primal-dual bandit push-sum algorithm that generates primal and dual variables with delayed feedback is used for the presented problem. Expected regret and expected constraint violation are proposed for measuring the performance of the algorithm, and both of them are shown to be sublinear with respect to the total iteration span
$T$
in this article. In the end, the optimization problem for the power grid is simulated to justify the proposed theoretical results.