Decentralized and Equitable Optimal Transport

Ivan Lau, Shiqian Ma, César A. Uribe
3/7/2024
math.OCcs.LG

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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/ε) 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/ε). This rate improves existing centralized algorithms, where the best iteration complexity obtained is O(1/ε^2).

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Cite this paper

@article{lau2024decentralized,
  title  = {Decentralized and Equitable Optimal Transport},
  author = {Ivan Lau and Shiqian Ma and César A. Uribe},
  year   = {2024},
  eprint = {2403.04259},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2403.04259v2}
}

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