Improved Convergence Rates for Distributed Resource Allocation

Angelia Nedic, Alex Olshevsky, Wei Shi

Abstract: In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation optimization problem over a connected network. By observing a connection between the resource allocation and the consensus optimization, we propose a novel class of algorithms for solving the resource allocation problem with improved convergence guarantees. Specifically, we introduce an algorithm for solving the resource allocation problem with an o(1/k) convergence rate when the agents' objective functions are generally convex and per agent local constraints are allowed; we then introduce a gradient-based algorithm for the case when per agent local constraints are absent and show that such scheme achieves geometric convergence with an improved scalability. We also provide a projection-gradient-based algorithm which can handle smooth objective and simple constraints more efficiently.