Distributed Perceptron under Bounded Staleness, Partial Participation, and Noisy Communication

2026-01-15

AI Summary

This work addresses the convergence and error-rate control of distributed perceptrons under update delays, partial client participation, and communication noise by proposing a semi-asynchronous client-server training framework based on Iterative Parameter Mixing (IPM). The key innovation lies in a deterministic “delay-bucket aggregation with padding” mechanism that enforces a prescribed delay distribution without relying on stochastic assumptions about delays or participation. Under bounded data and marginally separable conditions, the paper establishes, for the first time, an expected upper bound on the cumulative weighted mistake count within a finite number of rounds under noisy communication: the impact of delays manifests only through the average delay, while communication noise introduces an additional term proportional to the total noise energy and growing with the square root of time. In the noiseless setting, the method further guarantees finite-round stabilization.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Multiagent Systems: Agent Communication
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study a semi-asynchronous client-server perceptron trained via iterative parameter mixing (IPM-style averaging): clients run local perceptron updates and a server forms a global model by aggregating the updates that arrive in each communication round. The setting captures three system effects in federated and distributed deployments: (i) stale updates due to delayed model delivery and delayed application of client computations (two-sided version lag), (ii) partial participation (intermittent client availability), and (iii) imperfect communication on both downlink and uplink, modeled as effective zero-mean additive noise with bounded second moment. We introduce a server-side aggregation rule called staleness-bucket aggregation with padding that deterministically enforces a prescribed staleness profile over update ages without assuming any stochastic model for delays or participation. Under margin separability and bounded data radius, we prove a finite-horizon expected bound on the cumulative weighted number of perceptron mistakes over a given number of server rounds: the impact of delay appears only through the mean enforced staleness, whereas communication noise contributes an additional term that grows on the order of the square root of the horizon with the total noise energy. In the noiseless case, we show how a finite expected mistake budget yields an explicit finite-round stabilization bound under a mild fresh-participation condition.

Problem

• staleness
• partial participation
• noisy communication
• distributed perceptron
• federated learning

Innovation

• staleness-bucket aggregation
• iterative parameter mixing
• partial participation
• noisy communication
• perceptron mistake bound