Decentralized Max-Min Resource Allocation for Monotonic Utility Functions

Abstract

We consider a decentralized solution to max-min resource allocation for a multi-agent system. Limited resources are allocated to the agents in a network, each of which has a utility function monotonically increasing in its allocated resource. We aim at finding the allocation that maximizes the minimum utility among all agents. Although the problem can be easily solved with a centralized algorithm, developing a decentralized algorithm in absence of a central coordinator is challenging. We show that the decentralized max-min resource allocation problem can be nontrivially transformed to a canonical decentralized optimization. By using the gradient tracking technique in the decentralized optimization, we develop a decentralized algorithm to solve the max-min resource allocation. The algorithm converges to a solution at a linear convergence rate (in a log-scale) for strongly monotonic and Lipschitz continuous utility functions. Moreover, the algorithm is privacy-preserving since the agents only transmit encoded utilities and allocated resource to their intermediate neighbors. Numerical simulations show the advantage of our problem reformulation and validate the theoretical convergence result.