解决分布式最优传输的计算瓶颈，实现高效且精确的联邦式Sinkhorn算法。
Federated Sinkhorn
- 采用分片行矩阵的联邦框架，仅交换缩放向量片段。
- 多节点实验表明通信开销随节点数增加迅速成为瓶颈。
- 支持异步调度与隐私保护，适合大规模分布式学习场景。
当吉布斯核算子在c个工作节点间按行分区且无法集中时，我们研究了熵正则化最优传输的分布式Sinkhorn迭代。提出两种精确的同步协议：(i) 由Allgather实现的All-to-All方案，(ii) 由客户端到服务器发送与服务器广播实现的星型（参数服务器）方案。针对两者，我们在alpha-beta延迟-带宽模型下推导出每轮的计算、通信和内存开销闭式解，并证明在标准正性假设下，分布式迭代结果与集中式Sinkhorn一致。多节点CPU/GPU实验验证了模型，显示随着节点数增加，重复的全局缩放交换迅速成为主要瓶颈。此外，报告了一种可选的有界延迟异步调度及可选的通信日志缩放隐私测量层。
原文摘要 · Abstract (English)
We study distributed Sinkhorn iterations for entropy-regularized optimal transport when the Gibbs kernel operator is row-partitioned across c workers and cannot be centralized. We present Federated Sinkhorn, two exact synchronous protocols that exchange only scaling-vector slices: (i) an All-to-All scheme implemented by Allgather, and (ii) a Star (parameter-server) scheme implemented by client to server sends and server to client broadcasts. For both, we derive closed-form per-iteration compute, communication, and memory costs under an alpha-beta latency--bandwidth model, and show that the distributed iterates match centralized Sinkhorn under standard positivity assumptions. Multi-node CPU/GPU experiments validate the model and show that repeated global scaling exchange quickly becomes the dominant bottleneck as c increases. We also report an optional bounded-delay asynchronous schedule and an optional privacy measurement layer for communicated log-scalings.
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