An Algorithmic Foundation for Fair, Secure, and Differentially Private Distributed Discrete Optimal Transport

Jason Hughes, Fordham University


Optimal transport (OT) is a framework that can be used to facilitate the optimal allocation of resources in a network with multiple source and target nodes. To ease the computational complexity encountered by large-scale networks with a massive number of nodes, a distributed algorithm, based on the alternating direction method of multipliers (ADMM), is developed for computing the optimal transport strategy. However such a formulation lacks fairness, robustness and privacy considerations. Thus, there is an imperative need to develop distributed OT algorithms that allow for a more fair allocation of resources, accounts for possible deception attacks to the transport nodes and keeps nodes' sensitive information private during transport strategy updates. To achieve this goal, this thesis first incorporates a fairness metric into the objective function of the discrete OT problem and then leverages ADMM to develop a distributed algorithm. It then establishes a game-theoretic approach to counteract a deception attack where an attacker aims to compromise the transport plan. This formulation results in a min-max problem, and it can be solved in a distributed fashion to obtain a secure and resilient transport scheme. The distributed algorithms formed require communications on strategies between nodes during updates, which could potentially be intercepted and leveraged by an adversary, leading to private information being leaked. By incorporating differential privacy, the developed distributed algorithm guarantees the privacy of the sensitive information at each source and target node. All of the proposed algorithms are corroborated through case studies. The developed algorithmic foundation for fair, secure, and privacy-preserving discrete OT has broad applications to economics, machine learning and more.

Subject Area

Computer science|Applied Mathematics|Artificial intelligence

Recommended Citation

Hughes, Jason, "An Algorithmic Foundation for Fair, Secure, and Differentially Private Distributed Discrete Optimal Transport" (2021). ETD Collection for Fordham University. AAI28716383.