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AMSFL: Adaptive Multi-Step Federated Learning via Gradient Difference-Based Error Modeling

Ganglou Xu

TL;DR

Federated learning faces a trade-off between communication efficiency and model accuracy, especially under heterogeneous client data. The paper proposes Gradient Difference Approximation (GDA), a first-order method that estimates local update drift without computing Hessians, and embeds it into Adaptive Multi-Step Federated Learning (AMSFL) to dynamically choose the number of local steps under resource budgets. Theoretical analysis provides an error propagation framework, convergence guarantees, and a greedy time-budgeted step-allocation algorithm. Empirical results on NSL-KDD show AMSFL achieves higher global accuracy (around $0.9023$) and faster convergence (about $49$ seconds) with significantly reduced per-round time compared to baselines, validating the practical value of GDA-based adaptive scheduling in resource-constrained FL.

Abstract

Federated learning faces critical challenges in balancing communication efficiency and model accuracy. One key issue lies in the approximation of update errors without incurring high computational costs. In this paper, we propose a lightweight yet effective method called Gradient Difference Approximation (GDA), which leverages first-order information to estimate local error trends without computing the full Hessian matrix. The proposed method forms a key component of the Adaptive Multi-Step Federated Learning (AMSFL) framework and provides a unified error modeling strategy for large-scale multi-step adaptive training environments.

AMSFL: Adaptive Multi-Step Federated Learning via Gradient Difference-Based Error Modeling

TL;DR

Federated learning faces a trade-off between communication efficiency and model accuracy, especially under heterogeneous client data. The paper proposes Gradient Difference Approximation (GDA), a first-order method that estimates local update drift without computing Hessians, and embeds it into Adaptive Multi-Step Federated Learning (AMSFL) to dynamically choose the number of local steps under resource budgets. Theoretical analysis provides an error propagation framework, convergence guarantees, and a greedy time-budgeted step-allocation algorithm. Empirical results on NSL-KDD show AMSFL achieves higher global accuracy (around ) and faster convergence (about seconds) with significantly reduced per-round time compared to baselines, validating the practical value of GDA-based adaptive scheduling in resource-constrained FL.

Abstract

Federated learning faces critical challenges in balancing communication efficiency and model accuracy. One key issue lies in the approximation of update errors without incurring high computational costs. In this paper, we propose a lightweight yet effective method called Gradient Difference Approximation (GDA), which leverages first-order information to estimate local error trends without computing the full Hessian matrix. The proposed method forms a key component of the Adaptive Multi-Step Federated Learning (AMSFL) framework and provides a unified error modeling strategy for large-scale multi-step adaptive training environments.

Paper Structure

This paper contains 44 sections, 4 theorems, 68 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Error Modeling in Federated Learning
  4. First-Order Approximation Methods
  5. Multi-Step Local Training and Step Control Strategies
  6. Methodology
  7. Problem Formulation and Notation
  8. Error Modeling via Gradient Difference Approximation (GDA)
  9. Interpretation.
  10. Theoretical Results
  11. Assumptions.
  12. Adaptive Step Scheduling under Time Constraint
  13. Objective.
  14. Time Constraint.
  15. Optimization Problem.
  16. ...and 29 more sections

Key Result

Theorem 3.1

Under assumptions (A1)–(A4), the global error across communication rounds satisfies: Interpretation: The update consists of a descent term driven by the weighted global gradient, and a residual error determined by local training steps and curvature-induced drift.

Figures (1)

  • Figure 1: Accuracy Distribution across 50 Trials for Each Method

Theorems & Definitions (4)

  • Theorem 3.1: Error Recursion of AMSFL
  • Theorem 3.2: Linearized Form and Residual Convergence
  • Proposition 3.3: Approximation Error of GDA
  • Theorem 3.4: Optimal Local Step Allocation under Budget Constraint