Summary of Refined Analysis Of Federated Averaging’s Bias and Federated Richardson-romberg Extrapolation, by Paul Mangold et al.
Refined Analysis of Federated Averaging’s Bias and Federated Richardson-Romberg Extrapolation
by Paul Mangold, Alain Durmus, Aymeric Dieuleveut, Sergey Samsonov, Eric Moulines
First submitted to arxiv on: 2 Dec 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents an innovative analysis of FedAvg with constant step size, leveraging its Markov property. The researchers show that the global iterates of the algorithm converge to a stationary distribution and examine its resulting bias and variance relative to the problem’s solution. They provide a first-order expansion of the bias in both homogeneous and heterogeneous settings, revealing two distinct components: one dependent on stochastic gradient noise and another on client heterogeneity. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this paper, scientists study how an algorithm called FedAvg works when it has a constant step size. They show that the algorithm eventually reaches a point where it doesn’t change much and examine why its results might be biased or variable. The researchers find that this bias comes from two sources: random errors in the data and differences between individual users. To fix this issue, they propose a new algorithm that uses an old technique called Richardson-Romberg extrapolation. |
