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

Keval Jain, Anant Raj, Saurav Prakash, Girish Varma

TL;DR

This work addresses training a perceptron in a distributed, semi-asynchronous setting with partial participation and noisy communication. It introduces staleness-bucket aggregation with padding to deterministically enforce a prescribed staleness profile, enabling a finite-horizon bound on the cumulative weighted number of local perceptron mistakes where delay affects only the mean staleness and communication noise contributes an energy term $V$. The main result shows $\mathbb{E}[K_A]$ grows at most like $O(\sqrt{A})$ with an $O(1/A)$ term when noise is absent, and recovers the standard perceptron/IPM bounds in the appropriate limits; in the noiseless case, stabilization bounds are obtained under a fresh-participation condition. Practically, the framework supports robust distributed learning under delays and unreliable links, with implications for profile design and resilience in federated systems.

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.

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

TL;DR

This work addresses training a perceptron in a distributed, semi-asynchronous setting with partial participation and noisy communication. It introduces staleness-bucket aggregation with padding to deterministically enforce a prescribed staleness profile, enabling a finite-horizon bound on the cumulative weighted number of local perceptron mistakes where delay affects only the mean staleness and communication noise contributes an energy term . The main result shows grows at most like with an term when noise is absent, and recovers the standard perceptron/IPM bounds in the appropriate limits; in the noiseless case, stabilization bounds are obtained under a fresh-participation condition. Practically, the framework supports robust distributed learning under delays and unreliable links, with implications for profile design and resilience in federated systems.

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.
Paper Structure (32 sections, 4 theorems, 51 equations, 1 figure, 1 algorithm)

This paper contains 32 sections, 4 theorems, 51 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. System effects: staleness, partial participation, and noisy links
  3. Approach and contributions
  4. Notation
  5. System Model and Staleness-Profile IPM Perceptron
  6. Data and separability
  7. Two-sided staleness and server-enforced staleness profile
  8. Arrival (participation) sets
  9. Two-sided bounded staleness
  10. Client-side staleness and downlink noise
  11. Uplink noise
  12. Server-enforced staleness profile via padding
  13. Protocol requirements (minimal)
  14. Convexity
  15. Noise model
  16. ...and 17 more sections

Key Result

Theorem 1

Under margin separability eq:separable, $\left\lVert x\right\rVert\le R$, the bounded-staleness model eq:total-staleness, the noisy communication model eq:downlink--eq:noise-up, and the staleness-profile server update eq:update (with $\tau=\tau_{\mathrm{dl}}+\tau_{\mathrm{ul}}$), define the mean tot Then for every horizon $A\ge 1$, Consequently, In particular, when $V=0$ (no communication noise)

Figures (1)

  • Figure 1: Synthetic illustration of Theorem \ref{['thm:main']} for Algorithm \ref{['alg:main']}. (a) Noiseless links: different enforced staleness profiles $\bm{\alpha}$ (legend shows $\bar{s}$) lead to different cumulative weighted mistake levels. (b) Fixed profile: increasing noise energy $V$ increases $\mathbb{E}[K_A]$ approximately as $C+c\sqrt{A}$.

Theorems & Definitions (11)

  • Definition 1: Margin separability and radius
  • Definition 2: Conditional zero-mean bounded-variance effective channel noise
  • Theorem 1: Expected bound under two-sided staleness and noise
  • Remark 1: Special cases and interpretation
  • Lemma 1: Single-client perceptron progress (noisy stale initialization)
  • proof
  • Lemma 2: Stale-IPM inequalities under staleness-profile aggregation with padding
  • proof
  • Theorem 2: Finite-round stabilization in the noiseless case ($V=0$)
  • Remark 2: Noisy vs. noiseless within-bucket weighting
  • ...and 1 more