论文标题
与多个代理商的公平和最佳运输
Equitable and Optimal Transport with Multiple Agents
论文作者
论文摘要
当涉及多个成本时，我们引入了最佳运输问题的扩展。考虑到每个成本作为代理商，我们的目标是在代理之间平均分享将一个分配运送到另一个分配的工作。为此，我们最大程度地减少了工作最多的代理商的运输成本。另一个观点是，目标是根据代理商的异质偏好在代理之间平等分配商品。在这里，我们旨在最大化最不优势的代理商的效用。这是一个公平的分裂问题。像最佳传输一样，问题可以作为线性优化问题。当只有一个代理时，我们会恢复最佳运输问题。当考虑两种代理时，我们能够恢复由$α$-Hölder函数定义的整体概率指标，其中包括广为人知的达德利度量。据我们所知，这是达德利度量和最佳运输之间的第一次链接。我们提供了该问题的熵正规化，该熵可导致替代算法比标准线性程序快。
We introduce an extension of the Optimal Transport problem when multiple costs are involved. Considering each cost as an agent, we aim to share equally between agents the work of transporting one distribution to another. To do so, we minimize the transportation cost of the agent who works the most. Another point of view is when the goal is to partition equitably goods between agents according to their heterogeneous preferences. Here we aim to maximize the utility of the least advantaged agent. This is a fair division problem. Like Optimal Transport, the problem can be cast as a linear optimization problem. When there is only one agent, we recover the Optimal Transport problem. When two agents are considered, we are able to recover Integral Probability Metrics defined by $α$-Hölder functions, which include the widely-known Dudley metric. To the best of our knowledge, this is the first time a link is given between the Dudley metric and Optimal Transport. We provide an entropic regularization of that problem which leads to an alternative algorithm faster than the standard linear program.
