Decentralized and Equitable Optimal Transport
<|reference_start|>Decentralized and Equitable Optimal Transport: 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).<|reference_end|>
@article{lau2024decentralized,
    title={Decentralized and Equitable Optimal Transport},
    author={Ivan Lau, Shiqian Ma, C'esar A. Uribe},
    journal={2024 American Control Conference (ACC)},
    year={2024},
    doi={10.23919/ACC60939.2024.10644456},
    archivePrefix={arXiv},
    eprint={2403.04259},
    primaryClass={math.OC cs.LG}
}