Decentralized SGD and Average-direction SAM are Asymptotically Equivalent

Tongtian Zhu, Fengxiang He, Kaixuan Chen, Mingli Song, Dacheng Tao
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:43005-43036, 2023.

Abstract

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$\beta$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhu23e, title = {Decentralized {SGD} and Average-direction {SAM} are Asymptotically Equivalent}, author = {Zhu, Tongtian and He, Fengxiang and Chen, Kaixuan and Song, Mingli and Tao, Dacheng}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {43005--43036}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/zhu23e/zhu23e.pdf}, url = {https://proceedings.mlr.press/v202/zhu23e.html}, abstract = {Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$\beta$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios.} }
Endnote
%0 Conference Paper %T Decentralized SGD and Average-direction SAM are Asymptotically Equivalent %A Tongtian Zhu %A Fengxiang He %A Kaixuan Chen %A Mingli Song %A Dacheng Tao %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-zhu23e %I PMLR %P 43005--43036 %U https://proceedings.mlr.press/v202/zhu23e.html %V 202 %X Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$\beta$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios.
APA
Zhu, T., He, F., Chen, K., Song, M. & Tao, D.. (2023). Decentralized SGD and Average-direction SAM are Asymptotically Equivalent. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:43005-43036 Available from https://proceedings.mlr.press/v202/zhu23e.html.

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