Decentralized and Equitable Optimal Transport

Ivan Lau, Shiqian Ma, César A. Uribe

Abstract: This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each agent. We reformulate the D-OT problem as a constraint-coupled optimization problem and propose a single-loop decentralized algorithm with an iteration complexity of $O(1/\epsilon)$ that matches existing centralized first-order approaches. Moreover, we propose the decentralized equitable optimal transport (DE-OT) problem. In DE-OT, in addition to cooperatively designing a transportation plan that minimizes transportation costs, agents seek to ensure equity in their individual costs. The iteration complexity of the proposed method to solve DE-OT is also $O(1/\epsilon)$ . This rate improves existing centralized algorithms, where the best iteration complexity obtained is $O(1/\epsilon^{2})$ .