Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.14521 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916041834102784 |
|---|---|
| author | Baheri, Ali Vahid, Alireza |
| author_facet | Baheri, Ali Vahid, Alireza |
| contents | Distributed systems require fusing heterogeneous local probability distributions into a global summary over sparse and unreliable communication networks. Traditional consensus algorithms, which average distributions in Euclidean space, ignore their inherent geometric structure, leading to misleading results. Wasserstein barycenters offer a geometry-aware alternative by minimizing optimal transport costs, but their entropic approximations via the Sinkhorn algorithm typically require centralized coordination. This paper proposes a fully decentralized Sinkhorn algorithm that reformulates the centralized geometric mean as an arithmetic average in the log-domain, enabling approximation through local gossip protocols. Agents exchange log-messages with neighbors, interleaving consensus phases with local updates to mimic centralized iterations without a coordinator. To optimize bandwidth, we integrate event-triggered transmissions and b-bit quantization, providing tunable trade-offs between accuracy and communication while accommodating asynchrony and packet loss. Under mild assumptions, we prove convergence to a neighborhood of the centralized entropic barycenter, with bias linearly dependent on consensus tolerance, trigger threshold, and quantization error. Complexity scales near-linearly with network size. Simulations confirm near-centralized accuracy with significantly fewer messages, across various topologies and conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry-Aware Decentralized Sinkhorn for Wasserstein Barycenters Baheri, Ali Vahid, Alireza Systems and Control Distributed systems require fusing heterogeneous local probability distributions into a global summary over sparse and unreliable communication networks. Traditional consensus algorithms, which average distributions in Euclidean space, ignore their inherent geometric structure, leading to misleading results. Wasserstein barycenters offer a geometry-aware alternative by minimizing optimal transport costs, but their entropic approximations via the Sinkhorn algorithm typically require centralized coordination. This paper proposes a fully decentralized Sinkhorn algorithm that reformulates the centralized geometric mean as an arithmetic average in the log-domain, enabling approximation through local gossip protocols. Agents exchange log-messages with neighbors, interleaving consensus phases with local updates to mimic centralized iterations without a coordinator. To optimize bandwidth, we integrate event-triggered transmissions and b-bit quantization, providing tunable trade-offs between accuracy and communication while accommodating asynchrony and packet loss. Under mild assumptions, we prove convergence to a neighborhood of the centralized entropic barycenter, with bias linearly dependent on consensus tolerance, trigger threshold, and quantization error. Complexity scales near-linearly with network size. Simulations confirm near-centralized accuracy with significantly fewer messages, across various topologies and conditions. |
| title | Geometry-Aware Decentralized Sinkhorn for Wasserstein Barycenters |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.14521 |