Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks

Liyuan Liang, Xinyi Chen, Gan Luo, Kun Yuan
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:37100-37130, 2025.

Abstract

A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices, the row-stochastic scenario remains unexplored. This paper bridges this gap by introducing effective metrics to capture the influence of row-stochastic mixing matrices and establishing the first convergence lower bound for decentralized learning over row-stochastic networks. However, existing algorithms fail to attain this lower bound due to two key issues: deviation in the descent direction caused by the adapted gradient tracking (GT) and instability introduced by the Pull-Diag protocol. To address descent deviation, we propose a novel analysis framework demonstrating that Pull-Diag-GT achieves linear speedup—the first such result for row-stochastic decentralized optimization. Moreover, by incorporating a multi-step gossip (MG) protocol, we resolve the instability issue and attain the lower bound, achieving near-optimal complexity for decentralized optimization over row-stochastic networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liang25c, title = {Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks}, author = {Liang, Liyuan and Chen, Xinyi and Luo, Gan and Yuan, Kun}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {37100--37130}, 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/liang25c/liang25c.pdf}, url = {https://proceedings.mlr.press/v267/liang25c.html}, abstract = {A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices, the row-stochastic scenario remains unexplored. This paper bridges this gap by introducing effective metrics to capture the influence of row-stochastic mixing matrices and establishing the first convergence lower bound for decentralized learning over row-stochastic networks. However, existing algorithms fail to attain this lower bound due to two key issues: deviation in the descent direction caused by the adapted gradient tracking (GT) and instability introduced by the Pull-Diag protocol. To address descent deviation, we propose a novel analysis framework demonstrating that Pull-Diag-GT achieves linear speedup—the first such result for row-stochastic decentralized optimization. Moreover, by incorporating a multi-step gossip (MG) protocol, we resolve the instability issue and attain the lower bound, achieving near-optimal complexity for decentralized optimization over row-stochastic networks.} }
Endnote
%0 Conference Paper %T Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks %A Liyuan Liang %A Xinyi Chen %A Gan Luo %A Kun Yuan %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-liang25c %I PMLR %P 37100--37130 %U https://proceedings.mlr.press/v267/liang25c.html %V 267 %X A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices, the row-stochastic scenario remains unexplored. This paper bridges this gap by introducing effective metrics to capture the influence of row-stochastic mixing matrices and establishing the first convergence lower bound for decentralized learning over row-stochastic networks. However, existing algorithms fail to attain this lower bound due to two key issues: deviation in the descent direction caused by the adapted gradient tracking (GT) and instability introduced by the Pull-Diag protocol. To address descent deviation, we propose a novel analysis framework demonstrating that Pull-Diag-GT achieves linear speedup—the first such result for row-stochastic decentralized optimization. Moreover, by incorporating a multi-step gossip (MG) protocol, we resolve the instability issue and attain the lower bound, achieving near-optimal complexity for decentralized optimization over row-stochastic networks.
APA
Liang, L., Chen, X., Luo, G. & Yuan, K.. (2025). Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:37100-37130 Available from https://proceedings.mlr.press/v267/liang25c.html.

Related Material