Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for infere...
| Authors | Ilya Levin, Maksim Shuklin, Eric Moulines et al. |
|---|---|
| Primary category | stat.ML |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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