Age-of-information minimization with weight limits for semi-asynchronous online distributed optimization

We consider online distributed optimization where a server and multiple devices collaborate to minimize a sequence of time-varying global loss functions. To accommodate slow devices that may require multiple time slots to compute their local decisions, the server uses semi-asynchronous aggregation of the local decisions, which complicates device scheduling and performance optimization. In this work, we first analyze the convergence of semi-asynchronous aggregation in the presence of time-varying local update delays and loss-function weights. Our analysis leads to an online scheduling problem to minimize the accumulated age of information on the local decision updates, subject to individual long-term constraints on the total weights of the scheduled devices. We then design an efficient scheduling policy, termed Age-of-Information Minimization with Weight Limits (AIMWeL), through a modified Lyapunov optimization approach that uses the weighted sum of linear age-of-information values and quadratic virtual queues as a new Lyapunov function. We show that AIMWeL has bounded optimality ratio, via a novel double relaxation approach to handle the unique scheduling dependent communication indicator with time-varying probabilities of completing local decision update caused by semi asynchronous aggregation. When AIMWeL is applied to semi asynchronous federated learning, our simulation results based on standard image classification datasets demonstrate that AIMWeL uses significantly less time to reach the same classification accuracy achieved by the current best alternatives for both convex logistic regression and non-convex convolutional neural networks.