Refined Analysis of Federated Averaging and Federated Richardson-Romberg
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915685064507392 |
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| author | Mangold, Paul Durmus, Alain Dieuleveut, Aymeric Samsonov, Sergey Moulines, Eric |
| author_facet | Mangold, Paul Durmus, Alain Dieuleveut, Aymeric Samsonov, Sergey Moulines, Eric |
| contents | In this paper, we present a novel analysis of \FedAvg with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order bias expansion in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined Analysis of Federated Averaging and Federated Richardson-Romberg Mangold, Paul Durmus, Alain Dieuleveut, Aymeric Samsonov, Sergey Moulines, Eric Machine Learning Optimization and Control In this paper, we present a novel analysis of \FedAvg with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order bias expansion in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias. |
| title | Refined Analysis of Federated Averaging and Federated Richardson-Romberg |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2412.01389 |