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Asynchronous Diffusion Learning with Agent Subsampling and Local Updates

Elsa Rizk, Kun Yuan, Ali H. Sayed

TL;DR

This work studies asynchronous diffusion learning over networks where agents decide when to participate and which neighbors to consult, while performing local updates between communications. It develops a time-varying, random communication model and proves mean-square stability for the asynchronous ATC diffusion, deriving a closed-form MSD expression for the federated setting. The results show convergence to an $O(\mu)$-neighborhood of the weighted optimum $w^o$, with both the rate and accuracy governed by participation frequency and network connectivity. Numerical experiments on linear regression validate the theory and illustrate how partial participation and local updates influence convergence in practice.

Abstract

In this work, we examine a network of agents operating asynchronously, aiming to discover an ideal global model that suits individual local datasets. Our assumption is that each agent independently chooses when to participate throughout the algorithm and the specific subset of its neighbourhood with which it will cooperate at any given moment. When an agent chooses to take part, it undergoes multiple local updates before conveying its outcomes to the sub-sampled neighbourhood. Under this setup, we prove that the resulting asynchronous diffusion strategy is stable in the mean-square error sense and provide performance guarantees specifically for the federated learning setting. We illustrate the findings with numerical simulations.

Asynchronous Diffusion Learning with Agent Subsampling and Local Updates

TL;DR

This work studies asynchronous diffusion learning over networks where agents decide when to participate and which neighbors to consult, while performing local updates between communications. It develops a time-varying, random communication model and proves mean-square stability for the asynchronous ATC diffusion, deriving a closed-form MSD expression for the federated setting. The results show convergence to an -neighborhood of the weighted optimum , with both the rate and accuracy governed by participation frequency and network connectivity. Numerical experiments on linear regression validate the theory and illustrate how partial participation and local updates influence convergence in practice.

Abstract

In this work, we examine a network of agents operating asynchronously, aiming to discover an ideal global model that suits individual local datasets. Our assumption is that each agent independently chooses when to participate throughout the algorithm and the specific subset of its neighbourhood with which it will cooperate at any given moment. When an agent chooses to take part, it undergoes multiple local updates before conveying its outcomes to the sub-sampled neighbourhood. Under this setup, we prove that the resulting asynchronous diffusion strategy is stable in the mean-square error sense and provide performance guarantees specifically for the federated learning setting. We illustrate the findings with numerical simulations.
Paper Structure (7 sections, 4 theorems, 34 equations, 2 figures)

This paper contains 7 sections, 4 theorems, 34 equations, 2 figures.

Table of Contents

  1. Introduction and Related Material
  2. Asynchronous Network
  3. Problem Setup
  4. Stability Analysis
  5. Performance Analysis
  6. Experimental Results
  7. Conclusion

Key Result

Lemma 1

The gradient noise defined in eq:gradNoise has zero-mean and bounded second-order moment, namely: where $\beta_{s}^2$ and $\sigma_{s}^2$ are some constants.

Figures (2)

  • Figure 1: Illustration of an asynchronous network whose nodes and links change with time.
  • Figure 2: MSD curve for the asynchronous ATC diffusion algorithm.

Theorems & Definitions (8)

  • Lemma 1: First and second-order moments of gradient noise
  • proof
  • Theorem 1: Mean-square stability
  • proof
  • Theorem 2: Fourth-order stability
  • proof
  • Theorem 3: Steady-state MSD
  • proof