[Paper] Distributed Perceptron under Bounded Staleness, Partial Participation, and Noisy Communication

Source: arXiv - 2601.10705v1

Overview

This paper tackles a very practical problem: how to train a classic perceptron model when the training happens across many devices that are only intermittently online, receive delayed model updates, and communicate over noisy channels. By modeling these three real‑world frictions—stale updates, partial participation, and noisy communication—the authors derive provable guarantees for a federated‑style perceptron that still converges despite the messiness of the network.

Key Contributions

• Staleness‑bucket aggregation: a deterministic server‑side rule that groups client updates by their “age” (how many rounds they are behind) and pads missing updates, thereby enforcing a controllable staleness profile without any probabilistic delay assumptions.
• Theoretical mistake bound: under the standard margin‑separability assumption, the authors prove a finite‑horizon bound on the expected cumulative weighted perceptron mistakes. The bound separates the effect of delay (through the mean enforced staleness) from the effect of communication noise (which adds a √T‑type term).
• Stabilization guarantee for the noiseless case: when the downlink/uplink are perfect, the paper shows that a finite expected mistake budget translates into a concrete finite‑round convergence guarantee, assuming a mild “fresh‑participation” condition (each round sees at least one previously unseen client).
• Unified analysis of three system effects: rather than treating delay, dropout, and noise in isolation, the work provides a single analytical framework that captures all three simultaneously.

Methodology

1. Problem setup – A central server holds a global perceptron weight vector. In each communication round a subset of clients (the participants) receive the current global model, run a few local perceptron updates on their private data, and send back the resulting weight increment.
2. Modeling system imperfections
   • Staleness: Clients may apply updates that were computed on an older version of the global model. The “age” of an update is the number of server rounds it lags behind.
   • Partial participation: Only a random (or adversarial) subset of clients participates each round.
   • Noisy communication: Both the model sent to a client (downlink) and the update sent back (uplink) are corrupted by zero‑mean additive noise with bounded variance.
3. Staleness‑bucket aggregation – The server partitions incoming updates into buckets according to their age (0‑stale, 1‑stale, …). If a bucket is missing updates, the server pads it with zero vectors so that each bucket contributes a fixed weight to the global average. This deterministic padding forces the average staleness to stay within a prescribed bound.
4. Analysis technique – Extending the classic perceptron mistake‑bound proof, the authors track a potential function that mixes the global weight norm and the cumulative noise energy. By carefully bounding the contribution of stale updates (via the enforced mean staleness) and the noise term, they derive an expected mistake bound that holds for any sequence of participation patterns.

Results & Findings

In short, the perceptron remains robust: it tolerates delayed, intermittent, and noisy updates while still guaranteeing convergence rates comparable to the ideal synchronous, noise‑free setting.

Practical Implications

• Federated learning on edge devices – Many IoT or mobile scenarios involve devices that wake up sporadically and have flaky network connections. The bucket‑aggregation rule can be implemented on the server with minimal overhead, providing a principled way to handle out‑of‑date updates without discarding them.
• System design trade‑offs – Engineers can now budget staleness: by choosing how many buckets and how much padding to apply, they directly control the convergence slowdown. This gives a concrete knob for latency‑ vs‑accuracy trade‑offs in real deployments.
• Robustness to communication noise – The √T scaling suggests that modest amounts of quantization or channel noise will only mildly degrade performance, which validates the use of low‑precision or compressed communication schemes (e.g., sparsified updates).
• Extending to other linear models – Although the paper focuses on the perceptron, the analysis framework extends to any linear classifier trained via iterative parameter mixing (e.g., logistic regression with SGD). Developers can reuse the same server logic for a broader class of models.
• Simplified client logic – Clients do not need to track their own staleness or request fresh models; they simply run local updates on whatever model they have. This reduces client‑side complexity and battery consumption.

Limitations & Future Work

• Margin separability assumption – The theoretical guarantees hinge on the data being linearly separable with a positive margin, which rarely holds in noisy real‑world datasets. Extending the analysis to the soft‑margin or non‑separable case would broaden applicability.
• Fixed bucket structure – The current aggregation rule uses a static bucket configuration. Adaptive bucket sizing (e.g., based on observed network latency) could further improve performance but is not explored.
• Empirical validation – The paper provides a rigorous theoretical bound but lacks extensive experiments on real federated benchmarks (e.g., FEMNIST, Stack Overflow). Demonstrating the method’s practical speed‑up and accuracy trade‑offs would strengthen the contribution.
• Beyond perceptron – While the authors note that the technique could apply to other linear models, concrete extensions (e.g., to deep neural nets with non‑convex loss) remain an open research direction.

Overall, the work offers a solid theoretical foundation for building more resilient federated learning pipelines, especially when the underlying model is simple and linear. It opens the door for system‑aware algorithm design that embraces, rather than hides, the inevitable imperfections of distributed edge environments.

Authors

• Keval Jain
• Anant Raj
• Saurav Prakash
• Girish Varma

Paper Information

• arXiv ID: 2601.10705v1
• Categories: cs.LG
• Published: January 15, 2026
• PDF: Download PDF