Sharp Gaussian approximations for Decentralized Federated Learning

• URL: http://arxiv.org/abs/2505.08125v2
• Date: Wed, 22 Oct 2025 19:35:19 GMT
• Title: Sharp Gaussian approximations for Decentralized Federated Learning
• Authors: Soham Bonnerjee, Sayar Karmakar, Wei Biao Wu,
• Abstract summary: Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method.<n>We present two generalized Gaussian approximation results for local SGD and explore their implications.<n>The time-uniform approximations support bootstrap-based tests for detecting adversarial attacks.
• Score: 1.2489632787815885
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.

Related papers

• Uncertainty quantification for Markov chain induced martingales with application to temporal difference learning [55.197497603087065]
  We analyze the performance of the Temporal Difference (TD) learning algorithm with linear function approximations.<n>We establish novel and general high-dimensional concentration inequalities and Berry-Esseen bounds for vector-valued martingales induced by Markov chains.
  arXiv  Detail & Related papers  (2025-02-19T15:33:55Z)
• Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent [14.19520637866741]
  We establish the non-asymptotic validity of the multiplier bootstrap procedure for constructing confidence sets.<n>We derive approximation rates in convex distance of order up to $1/sqrtn$.
  arXiv  Detail & Related papers  (2025-02-10T17:49:05Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates [5.13323375365494]
  We provide theoretical guarantees for the convergence behaviour of diffusion-based generative models under strongly log-concave data.<n>Our class of functions used for score estimation is made of Lipschitz continuous functions avoiding any Lipschitzness assumption on the score function.<n>This approach yields the best known convergence rate for our sampling algorithm.
  arXiv  Detail & Related papers  (2023-11-22T18:40:45Z)
• Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator [0.0]
  In this paper, we investigate the theoretical properties of gradient descent (SGD) for statistical inference in the context of convex problems. We propose two coferential procedures which may contain multiple error minima.
  arXiv  Detail & Related papers  (2023-06-03T22:08:10Z)
• A Unified Momentum-based Paradigm of Decentralized SGD for Non-Convex Models and Heterogeneous Data [0.261072980439312]
  We propose a unified paradigm called U.MP, D-MP and GT-D, which provides a convergence guarantee for non general objectives. In theory we provide the convergence analysis objectives two approaches for these non-MP algorithms.
  arXiv  Detail & Related papers  (2023-03-01T02:13:22Z)
• Optimal Scaling for Locally Balanced Proposals in Discrete Spaces [65.14092237705476]
  We show that efficiency of Metropolis-Hastings (M-H) algorithms in discrete spaces can be characterized by an acceptance rate that is independent of the target distribution. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces.
  arXiv  Detail & Related papers  (2022-09-16T22:09:53Z)
• Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithms [14.174806471635403]
  We consider approximations of sampling algorithms, such as Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD) We observe that the noise introduced by the approximation is nearly Gaussian due to the Central Limit Theorem (CLT) while the driving Brownian motion is exactly Gaussian. We harness this structure to absorb the approximation error inside the diffusion process, and obtain improved convergence guarantees for these algorithms.
  arXiv  Detail & Related papers  (2022-06-08T10:17:40Z)
• Gaussian Graphical Models as an Ensemble Method for Distributed Gaussian Processes [8.4159776055506]
  We propose a novel approach for aggregating the Gaussian experts' predictions by Gaussian graphical model (GGM) We first estimate the joint distribution of latent and observed variables using the Expectation-Maximization (EM) algorithm. Our new method outperforms other state-of-the-art DGP approaches.
  arXiv  Detail & Related papers  (2022-02-07T15:22:56Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• ROOT-SGD: Sharp Nonasymptotics and Near-Optimal Asymptotics in a Single Algorithm [71.13558000599839]
  We study the problem of solving strongly convex and smooth unconstrained optimization problems using first-order algorithms. We devise a novel, referred to as Recursive One-Over-T SGD, based on an easily implementable, averaging of past gradients. We prove that it simultaneously achieves state-of-the-art performance in both a finite-sample, nonasymptotic sense and an sense.
  arXiv  Detail & Related papers  (2020-08-28T14:46:56Z)
• Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Condition [52.08417569774822]
  This paper focuses on methods for solving smooth non-concave min-max problems, which have received increasing attention due to deep learning (e.g., deep AUC)
  arXiv  Detail & Related papers  (2020-06-12T00:32:21Z)
• A Unified Theory of Decentralized SGD with Changing Topology and Local Updates [70.9701218475002]
  We introduce a unified convergence analysis of decentralized communication methods. We derive universal convergence rates for several applications. Our proofs rely on weak assumptions.
  arXiv  Detail & Related papers  (2020-03-23T17:49:15Z)
• Distributional Robustness and Regularization in Reinforcement Learning [62.23012916708608]
  We introduce a new regularizer for empirical value functions and show that it lower bounds the Wasserstein distributionally robust value function. It suggests using regularization as a practical tool for dealing with $textitexternal uncertainty$ in reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-05T19:56:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.