Welfare Measure for Resource Allocation with Algorithmic Implementation: Beyond Average and Max-Min

TL;DR

This paper introduces an axiomatic framework for measuring system welfare in resource allocation, unifying existing principles like average and max-min fairness, and proposing new optimality notions with practical algorithms and applications.

Contribution

It develops a unifying axiomatic approach to welfare measurement, introduces new optimality concepts, and provides a gradient-based method with theoretical guarantees for resource allocation.

Findings

Unified welfare measure encompassing existing and new optimality principles

Gradient-based algorithm with proven convergence guarantees

Successful application to power control in wireless networks

Abstract

In this work, we propose an axiomatic approach for measuring the performance/welfare of a system consisting of concurrent agents in a resource-driven system. Our approach provides a unifying view on popular system optimality principles, such as the maximal average/total utilities and the max-min fairness. Moreover, it gives rise to other system optimality notions that have not been fully exploited yet, such as the maximal lowest total subgroup utilities. For the axiomatically defined welfare measures, we provide a generic gradient-based method to find an optimal resource allocation and present a theoretical guarantee for its success. Lastly, we demonstrate the power of our approach through the power control application in wireless networks.