Decentralized and Equitable Optimal Transport

• URL: http://arxiv.org/abs/2403.04259v2
• Date: Tue, 12 Mar 2024 04:02:49 GMT
• Title: Decentralized and Equitable Optimal Transport
• Authors: Ivan Lau, Shiqian Ma, C\'esar A. Uribe
• Abstract summary: We reformulate the D-OT problem as a constraint-coupled optimization problem. We propose a single-loop decentralized algorithm with an iteration complexity of O(1/epsilon) that matches existing centralized first-order approaches.
• Score: 5.035903052108509
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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).

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