Abstract-We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network in which the agents communicate with their neighbors and perform local computation. In the proposed algorithm, each agent can compute and communicate independently at different times, for different durations, with the information it has even if the latest information from its neighbors is not yet available. Such an asynchronous algorithm reduces the time that agents would otherwise waste idle because of communication delays or because their neighbors are slower. It also eliminates the need for a global clock for synchronization. Mathematically, the algorithm involves both primal and dual variables, uses fixed step-size parameters, and provably converges to the exact solution under a random agent assumption and both bounded and unbounded delay assumptions. When running synchronously, the algorithm performs just as well as existing competitive synchronous algorithms such as PG-EXTRA, which diverges without synchronization. Numerical experiments confirm the theoretical findings and illustrate the performance of the proposed algorithm.
For the decentralized, asynchronous consensus optimization, REF extends the existing PG-EXTRA and proves convergence of the algorithm.
Decentralized Consensus Optimization With Asynchrony and Delays
IEEE Transactions on Signal and Information Processing over Networks
IEEE Transactions on Signal and Information Processing over Networks
Mathematics Computer Science