Diffusion Learning with Partial Agent Participation and Local Updates

TL;DR

This work extends diffusion learning to fully decentralized settings with two practical enhancements: local updates to reduce communication and partial agent participation to handle intermittent device availability. The authors establish mean-square stability and derive a tight M S D expression, revealing how the number of local updates and activation probabilities influence steady-state performance. They show that, in expectation, the algorithm can drift to a modified objective when participation is imperfect, and provide a drift-correction scheme when participation rates are known. The framework unifies several existing methods (e.g., FedAvg, standard and asynchronous diffusion) as special cases and is validated on a linear regression task, demonstrating accurate MSD predictions and clear trade-offs for practical deployment in edge networks.

Abstract

Diffusion learning is a framework that endows edge devices with advanced intelligence. By processing and analyzing data locally and allowing each agent to communicate with its immediate neighbors, diffusion effectively protects the privacy of edge devices, enables real-time response, and reduces reliance on central servers. However, traditional diffusion learning relies on communication at every iteration, leading to communication overhead, especially with large learning models. Furthermore, the inherent volatility of edge devices, stemming from power outages or signal loss, poses challenges to reliable communication between neighboring agents. To mitigate these issues, this paper investigates an enhanced diffusion learning approach incorporating local updates and partial agent participation. Local updates will curtail communication frequency, while partial agent participation will allow for the inclusion of agents based on their availability. We prove that the resulting algorithm is stable in the mean-square error sense and provide a tight analysis of its Mean-Square-Deviation (MSD) performance. Various numerical experiments are conducted to illustrate our theoretical findings.

Figures (7)

• Figure 1: Illustration of the time scales for diffusion learning with local updates, i.e., recursion \ref{['eq:diff-compact-local-update']}.
• Figure 2: Evolution of the network topology during the $i$-th and $(i+1)$-th block index. The first figure shows the underlying graph. The second and fourth figures depict the topology during the local update steps, with all links turned off and inactive agents dimmed. The third and fifth figures illustrate the topology during the collaboration stage, where only the links between active agents are maintained.
• Figure 3: Suppose each agent $k$ starts at the optimal solution, i.e., $w_{k,i} = w^o$. The one-step update $\bar{w}_{i+1}$ will remain at the optimal solution only if the condition $\frac{1}{K} \sum_{k=1}^K q_k \nabla J_k(w^o) = 0$ is satisfied. This implies that $w^o$ is, in fact, the optimal solution to problem \ref{['eq:optMod']}.
• Figure 4: The underlying network.
• Figure 5: The steady-state performance of Algorithm \ref{['alg:assynATC']} with local updates and partial agent participation matches with the theoretical MSD expression \ref{['eq:MSD-expre']} established in Theorem \ref{['thrm:MSD']}.

Theorems & Definitions (17)

• Lemma 1: Network topology in expectation
• proof
• Lemma 2: Second-order Gradient noise
• proof
• Lemma 3: Fourth-order Gradient noise
• proof
• Theorem 1: Second-order stability
• proof
• Theorem 2: Fourth-order stability
• proof