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| Autori principali: | , , , , , |
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| Natura: | Preprint |
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2022
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2206.12680 |
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| _version_ | 1866909576974041088 |
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| author | Zhu, Tongtian He, Fengxiang Zhang, Lan Niu, Zhengyang Song, Mingli Tao, Dacheng |
| author_facet | Zhu, Tongtian He, Fengxiang Zhang, Lan Niu, Zhengyang Song, Mingli Tao, Dacheng |
| contents | This paper studies the algorithmic stability and generalizability of decentralized stochastic gradient descent (D-SGD). We prove that the consensus model learned by D-SGD is $\mathcal{O}{(N^{-1}+m^{-1} +λ^2)}$-stable in expectation in the non-convex non-smooth setting, where $N$ is the total sample size, $m$ is the worker number, and $1+λ$ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an $\mathcal{O}{(N^{-(1+α)/2}+ m^{-(1+α)/2}+λ^{1+α} + ϕ_{\mathcal{S}})}$ in-average generalization bound, which is non-vacuous even when $λ$ is closed to $1$, in contrast to vacuous as suggested by existing literature on the projected version of D-SGD. Our theory indicates that the generalizability of D-SGD is positively correlated with the spectral gap, and can explain why consensus control in initial training phase can ensure better generalization. Experiments of VGG-11 and ResNet-18 on CIFAR-10, CIFAR-100 and Tiny-ImageNet justify our theory. To our best knowledge, this is the first work on the topology-aware generalization of vanilla D-SGD. Code is available at https://github.com/Raiden-Zhu/Generalization-of-DSGD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12680 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Topology-aware Generalization of Decentralized SGD Zhu, Tongtian He, Fengxiang Zhang, Lan Niu, Zhengyang Song, Mingli Tao, Dacheng Machine Learning This paper studies the algorithmic stability and generalizability of decentralized stochastic gradient descent (D-SGD). We prove that the consensus model learned by D-SGD is $\mathcal{O}{(N^{-1}+m^{-1} +λ^2)}$-stable in expectation in the non-convex non-smooth setting, where $N$ is the total sample size, $m$ is the worker number, and $1+λ$ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an $\mathcal{O}{(N^{-(1+α)/2}+ m^{-(1+α)/2}+λ^{1+α} + ϕ_{\mathcal{S}})}$ in-average generalization bound, which is non-vacuous even when $λ$ is closed to $1$, in contrast to vacuous as suggested by existing literature on the projected version of D-SGD. Our theory indicates that the generalizability of D-SGD is positively correlated with the spectral gap, and can explain why consensus control in initial training phase can ensure better generalization. Experiments of VGG-11 and ResNet-18 on CIFAR-10, CIFAR-100 and Tiny-ImageNet justify our theory. To our best knowledge, this is the first work on the topology-aware generalization of vanilla D-SGD. Code is available at https://github.com/Raiden-Zhu/Generalization-of-DSGD. |
| title | Topology-aware Generalization of Decentralized SGD |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2206.12680 |