HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation

Qiyuan Chen, Xian Wu, Yi Wang, Xianhao Chen
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:17527-17551, 2026.

Abstract

Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose Hybrid-Order Split Federated Learning (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26fd, title = {{HO}-{SFL}: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation}, author = {Chen, Qiyuan and Wu, Xian and Wang, Yi and Chen, Xianhao}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {17527--17551}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26fd/chen26fd.pdf}, url = {https://proceedings.mlr.press/v306/chen26fd.html}, abstract = {Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose Hybrid-Order Split Federated Learning (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.} }
Endnote
%0 Conference Paper %T HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation %A Qiyuan Chen %A Xian Wu %A Yi Wang %A Xianhao Chen %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26fd %I PMLR %P 17527--17551 %U https://proceedings.mlr.press/v306/chen26fd.html %V 306 %X Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose Hybrid-Order Split Federated Learning (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.
APA
Chen, Q., Wu, X., Wang, Y. & Chen, X.. (2026). HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:17527-17551 Available from https://proceedings.mlr.press/v306/chen26fd.html.

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