Riemannian Diffusion Adaptation for Distributed Optimization on Manifolds

Xiuheng Wang, Ricardo Augusto Borsoi, Cédric Richard, Ali H. Sayed
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:62401-62422, 2025.

Abstract

Online distributed optimization is particularly useful for solving optimization problems with streaming data collected by multiple agents over a network. When the solutions lie on a Riemannian manifold, such problems become challenging to solve, particularly when efficiency and continuous adaptation are required. This work tackles these challenges and devises a diffusion adaptation strategy for decentralized optimization over general manifolds. A theoretical analysis shows that the proposed algorithm is able to approach network agreement after sufficient iterations, which allows a non-asymptotic convergence result to be derived. We apply the algorithm to the online decentralized principal component analysis problem and Gaussian mixture model inference. Experimental results with both synthetic and real data illustrate its performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25h, title = {{R}iemannian Diffusion Adaptation for Distributed Optimization on Manifolds}, author = {Wang, Xiuheng and Borsoi, Ricardo Augusto and Richard, C\'{e}dric and Sayed, Ali H.}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {62401--62422}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wang25h/wang25h.pdf}, url = {https://proceedings.mlr.press/v267/wang25h.html}, abstract = {Online distributed optimization is particularly useful for solving optimization problems with streaming data collected by multiple agents over a network. When the solutions lie on a Riemannian manifold, such problems become challenging to solve, particularly when efficiency and continuous adaptation are required. This work tackles these challenges and devises a diffusion adaptation strategy for decentralized optimization over general manifolds. A theoretical analysis shows that the proposed algorithm is able to approach network agreement after sufficient iterations, which allows a non-asymptotic convergence result to be derived. We apply the algorithm to the online decentralized principal component analysis problem and Gaussian mixture model inference. Experimental results with both synthetic and real data illustrate its performance.} }
Endnote
%0 Conference Paper %T Riemannian Diffusion Adaptation for Distributed Optimization on Manifolds %A Xiuheng Wang %A Ricardo Augusto Borsoi %A Cédric Richard %A Ali H. Sayed %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wang25h %I PMLR %P 62401--62422 %U https://proceedings.mlr.press/v267/wang25h.html %V 267 %X Online distributed optimization is particularly useful for solving optimization problems with streaming data collected by multiple agents over a network. When the solutions lie on a Riemannian manifold, such problems become challenging to solve, particularly when efficiency and continuous adaptation are required. This work tackles these challenges and devises a diffusion adaptation strategy for decentralized optimization over general manifolds. A theoretical analysis shows that the proposed algorithm is able to approach network agreement after sufficient iterations, which allows a non-asymptotic convergence result to be derived. We apply the algorithm to the online decentralized principal component analysis problem and Gaussian mixture model inference. Experimental results with both synthetic and real data illustrate its performance.
APA
Wang, X., Borsoi, R.A., Richard, C. & Sayed, A.H.. (2025). Riemannian Diffusion Adaptation for Distributed Optimization on Manifolds. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:62401-62422 Available from https://proceedings.mlr.press/v267/wang25h.html.

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