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Taming Subnet-Drift in D2D-Enabled Fog Learning: A Hierarchical Gradient Tracking Approach

Evan Chen, Shiqiang Wang, Christopher G. Brinton

TL;DR

This work tackles subnet-drift in SD-FL by introducing Semi-Decentralized Gradient Tracking (SD-GT), which employs dual gradient-tracking terms to stabilize updates across the D2D and DS communication layers over two timescales. It provides Lyapunov-based convergence bounds for both non-convex and strongly convex objectives and proposes a co-optimization framework to trade learning speed against communication cost via subnet sampling and D2D rounds. Theoretical results are corroborated by extensive experiments on real-world and synthetic datasets, showing substantial improvements in model quality and communication efficiency over SD-FL and gradient-tracking baselines. The approach enables robust, scalable fog-learning deployments with tunable efficiency suitable for heterogeneous networks.

Abstract

Federated learning (FL) encounters scalability challenges when implemented over fog networks. Semi-decentralized FL (SD-FL) proposes a solution that divides model cooperation into two stages: at the lower stage, device-to-device (D2D) communications is employed for local model aggregations within subnetworks (subnets), while the upper stage handles device-server (DS) communications for global model aggregations. However, existing SD-FL schemes are based on gradient diversity assumptions that become performance bottlenecks as data distributions become more heterogeneous. In this work, we develop semi-decentralized gradient tracking (SD-GT), the first SD-FL methodology that removes the need for such assumptions by incorporating tracking terms into device updates for each communication layer. Analytical characterization of SD-GT reveals convergence upper bounds for both non-convex and strongly-convex problems, for a suitable choice of step size. We employ the resulting bounds in the development of a co-optimization algorithm for optimizing subnet sampling rates and D2D rounds according to a performance-efficiency trade-off. Our subsequent numerical evaluations demonstrate that SD-GT obtains substantial improvements in trained model quality and communication cost relative to baselines in SD-FL and gradient tracking on several datasets.

Taming Subnet-Drift in D2D-Enabled Fog Learning: A Hierarchical Gradient Tracking Approach

TL;DR

This work tackles subnet-drift in SD-FL by introducing Semi-Decentralized Gradient Tracking (SD-GT), which employs dual gradient-tracking terms to stabilize updates across the D2D and DS communication layers over two timescales. It provides Lyapunov-based convergence bounds for both non-convex and strongly convex objectives and proposes a co-optimization framework to trade learning speed against communication cost via subnet sampling and D2D rounds. Theoretical results are corroborated by extensive experiments on real-world and synthetic datasets, showing substantial improvements in model quality and communication efficiency over SD-FL and gradient-tracking baselines. The approach enables robust, scalable fog-learning deployments with tunable efficiency suitable for heterogeneous networks.

Abstract

Federated learning (FL) encounters scalability challenges when implemented over fog networks. Semi-decentralized FL (SD-FL) proposes a solution that divides model cooperation into two stages: at the lower stage, device-to-device (D2D) communications is employed for local model aggregations within subnetworks (subnets), while the upper stage handles device-server (DS) communications for global model aggregations. However, existing SD-FL schemes are based on gradient diversity assumptions that become performance bottlenecks as data distributions become more heterogeneous. In this work, we develop semi-decentralized gradient tracking (SD-GT), the first SD-FL methodology that removes the need for such assumptions by incorporating tracking terms into device updates for each communication layer. Analytical characterization of SD-GT reveals convergence upper bounds for both non-convex and strongly-convex problems, for a suitable choice of step size. We employ the resulting bounds in the development of a co-optimization algorithm for optimizing subnet sampling rates and D2D rounds according to a performance-efficiency trade-off. Our subsequent numerical evaluations demonstrate that SD-GT obtains substantial improvements in trained model quality and communication cost relative to baselines in SD-FL and gradient tracking on several datasets.
Paper Structure (18 sections, 11 theorems, 41 equations, 5 figures, 1 algorithm)

This paper contains 18 sections, 11 theorems, 41 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Semi-Decentralized FL and Subnet-Drift
  3. Outline and Summary of Contributions
  4. Related Works
  5. Proposed Method
  6. Network Model and Timescales
  7. Learning Model
  8. Connection with Existing Methods
  9. Analysis and Optimization
  10. Convergence Analysis Assumptions
  11. Convergence Analysis Results
  12. Learning-Efficiency Co-Optimization
  13. Numerical Evaluation
  14. Experimental Setup
  15. Results and Discussion
  16. ...and 3 more sections

Key Result

Theorem 1

(Non-convex) Under Assumptions asmp1, asmp2, and assmp3. Let $\beta_{s} = \frac{m_{s} - h_{s}}{m_{s}}$ be the ratio of unsampled clients from each subnet, and define the sample-wise mixing rate term $\phi_{s} = (1 - \beta_{s}^2)$ . Define $p = \min(\phi_{1} , \ldots, \phi_{S})\in (0,1]$, and $q = \m

Figures (5)

  • Figure 1: Illustration of semi-decentralized FL. Clients in each subnet communicate via iterative low-cost D2D communications to conduct local aggregations. Once they have converged towards a consensus within the subnet, the central server conducts a global aggregation across sampled devices using DS communication.
  • Figure 2: An illustration of how SD-GT deals with subnet-drifting. With the introduction of in-subnet GT term $z_i^t$, all clients within each subnet are able to converge towards a consensual location of the subnet. And the inter-subnet GT term $y_i^t$ corrects the update direction of the whole subnet so that it no longer converges towards the optimal solution $x_{\mathcal{C}_s}^*$of the subnet $\mathcal{C}_s$ but the optimal solution $x^*$ of the whole network.
  • Figure 3: Experimental results on real-world datasets ($\frac{h_{s}}{m_{s}} = 40\%$). By fixing the sampling rate for each subnet to $40$ percent and observe the effect of performing multiple D2D communication rounds, we see that our algorithm SD-GT gains the most improvement from increasing the D2D rounds. The advantage of our method can still be observed even if we double the number of clients in the system.
  • Figure 4: Experimental results from synthetic dataset $(K = 40)$. By fixing the number of D2D rounds performed between two global aggregations, we see that our algorithm SD-GT is able to improve from increasing the sampling rate of each subnet while maintaining linear rate.
  • Figure 5: Experiments on the proposed co-optimization algorithm. When $\delta$ is small (D2D communication is cheap), the co-optimization algorithm is able to choose the sample rate and the number of D2D communication rounds such that more improvement is obtained using the same amount of communication.

Theorems & Definitions (22)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Theorem 2
  • proof
  • Corollary 2
  • proof
  • Lemma 1
  • proof
  • ...and 12 more