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Improved Generalization Bounds for Communication Efficient Federated Learning

Peyman Gholami, Hulya Seferoglu

TL;DR

The paper tackles the high communication cost of federated learning by deriving tighter generalization bounds for one-round and R-round FedAvg, tying generalization to local client performance and data heterogeneity. It then offers a representation-learning perspective, showing that aggregating the representation extractor less frequently can yield more generalizable models in non-iid settings. Building on this, the authors propose FedALS, a Federated Learning with Adaptive Local Steps algorithm that differentially schedules local updates for the representation extractor and the head to reduce communication while preserving or improving generalization. Empirical results on image tasks (e.g., CIFAR-10/100, SVHN) and language tasks (OPT-125M fine-tuning) demonstrate FedALS’s benefits in non-iid regimes, with negligible gains in iid settings and favorable comparisons to SCAFFOLD. Overall, the work provides a principled link between generalization theory and practical FL design, offering a path toward efficient, scalable learning under data heterogeneity.

Abstract

This paper focuses on reducing the communication cost of federated learning by exploring generalization bounds and representation learning. We first characterize a tighter generalization bound for one-round federated learning based on local clients' generalizations and heterogeneity of data distribution (non-iid scenario). We also characterize a generalization bound in R-round federated learning and its relation to the number of local updates (local stochastic gradient descents (SGDs)). Then, based on our generalization bound analysis and our representation learning interpretation of this analysis, we show for the first time that less frequent aggregations, hence more local updates, for the representation extractor (usually corresponds to initial layers) leads to the creation of more generalizable models, particularly for non-iid scenarios. We design a novel Federated Learning with Adaptive Local Steps (FedALS) algorithm based on our generalization bound and representation learning analysis. FedALS employs varying aggregation frequencies for different parts of the model, so reduces the communication cost. The paper is followed with experimental results showing the effectiveness of FedALS.

Improved Generalization Bounds for Communication Efficient Federated Learning

TL;DR

The paper tackles the high communication cost of federated learning by deriving tighter generalization bounds for one-round and R-round FedAvg, tying generalization to local client performance and data heterogeneity. It then offers a representation-learning perspective, showing that aggregating the representation extractor less frequently can yield more generalizable models in non-iid settings. Building on this, the authors propose FedALS, a Federated Learning with Adaptive Local Steps algorithm that differentially schedules local updates for the representation extractor and the head to reduce communication while preserving or improving generalization. Empirical results on image tasks (e.g., CIFAR-10/100, SVHN) and language tasks (OPT-125M fine-tuning) demonstrate FedALS’s benefits in non-iid regimes, with negligible gains in iid settings and favorable comparisons to SCAFFOLD. Overall, the work provides a principled link between generalization theory and practical FL design, offering a path toward efficient, scalable learning under data heterogeneity.

Abstract

This paper focuses on reducing the communication cost of federated learning by exploring generalization bounds and representation learning. We first characterize a tighter generalization bound for one-round federated learning based on local clients' generalizations and heterogeneity of data distribution (non-iid scenario). We also characterize a generalization bound in R-round federated learning and its relation to the number of local updates (local stochastic gradient descents (SGDs)). Then, based on our generalization bound analysis and our representation learning interpretation of this analysis, we show for the first time that less frequent aggregations, hence more local updates, for the representation extractor (usually corresponds to initial layers) leads to the creation of more generalizable models, particularly for non-iid scenarios. We design a novel Federated Learning with Adaptive Local Steps (FedALS) algorithm based on our generalization bound and representation learning analysis. FedALS employs varying aggregation frequencies for different parts of the model, so reduces the communication cost. The paper is followed with experimental results showing the effectiveness of FedALS.
Paper Structure (23 sections, 8 theorems, 43 equations, 3 figures, 3 tables, 4 algorithms)

This paper contains 23 sections, 8 theorems, 43 equations, 3 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background and Problem Statement
  4. Preliminaries and Notation
  5. Generalization Error
  6. Federated Learning
  7. Representation Learning
  8. Improved Generalization Bounds
  9. One-Round Generalization Bound
  10. $R-$Round Generalization Bound
  11. Representation Learning Interpretation of R-Round Generalization Bound
  12. FedALS: Federated Learning with Adaptive Local Steps
  13. Experimental Results
  14. FedALS in non-iid Setting
  15. FedALS in iid Setting
  16. ...and 8 more sections

Key Result

Theorem 4.1

Let $l(M_{{\boldsymbol{\theta}_{}}},\boldsymbol{z})$ be $\mu$-strongly convex and $L$-smooth in $M_{{\boldsymbol{\theta}_{}}}$. $M_{{\boldsymbol{\theta}_{}}_k}=\mathcal{A}_k(\boldsymbol{S}_{k})$ represents the model obtained from Empirical Risk Minimization (ERM) algorithm on local dataset $\boldsym where $\delta_{k,\mathcal{A}}(\boldsymbol{S}_{}) = R_{\boldsymbol{S}_{k}}(\mathcal{A}(\boldsymbol{

Figures (3)

  • Figure 1: Average consensus distance over time for different layers, measured while training a ResNet-$20$ by FedAvg on CIFAR-$10$ with $5$ clients with non-iid data distribution over clients ($2$ classes per client). The early layers responsible for extracting representations exhibit lower levels of consensus distance.
  • Figure 2: Training ResNet-$20$ on SVHN.
  • Figure 3: Fine-tuning OPT-$125$M on MultiNLI.

Theorems & Definitions (17)

  • Example 1
  • Theorem 4.1
  • Remark 4.2
  • Theorem 4.3
  • Remark 5.1
  • Lemma A.1: Leave-one-out
  • proof
  • Theorem A.2
  • proof
  • Theorem B.1
  • ...and 7 more