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Distributed Experimental Design Networks

Yuanyuan Li, Lili Su, Carlee Joe-Wong, Edmund Yeh, Stratis Ioannidis

TL;DR

The paper addresses rate-allocation for data streams in distributed experimental design networks with multicast constraints, proving the learning-quality objective is non-convex yet continuous DR-submodular. It gives a centralized FW-based algorithm with a $1-1/e$ guarantee and a scalable distributed primal-dual FW variant that preserves this guarantee under a differentiable constraint relaxation. The work extends to Gaussian sources and heterogeneous noise, providing unbiased gradient estimators with probabilistic error bounds and extensive simulations on synthetic and backbone topologies showing near-centralized performance. The results demonstrate that multicast-based design substantially improves throughput and model quality, offering practical avenues for edge-enabled distributed learning. Limitations include synchronization requirements, motivating future work on asynchronous schemes and shadow-price-based gradient estimation, along with publicly available code and data.

Abstract

As edge computing capabilities increase, model learning deployments in diverse edge environments have emerged. In experimental design networks, introduced recently, network routing and rate allocation are designed to aid the transfer of data from sensors to heterogeneous learners. We design efficient experimental design network algorithms that are (a) distributed and (b) use multicast transmissions. This setting poses significant challenges as classic decentralization approaches often operate on (strictly) concave objectives under differentiable constraints. In contrast, the problem we study here has a non-convex, continuous DR-submodular objective, while multicast transmissions naturally result in non-differentiable constraints. From a technical standpoint, we propose a distributed Frank-Wolfe and a distributed projected gradient ascent algorithm that, coupled with a relaxation of non-differentiable constraints, yield allocations within a $1-1/e$ factor from the optimal. Numerical evaluations show that our proposed algorithms outperform competitors with respect to model learning quality.

Distributed Experimental Design Networks

TL;DR

The paper addresses rate-allocation for data streams in distributed experimental design networks with multicast constraints, proving the learning-quality objective is non-convex yet continuous DR-submodular. It gives a centralized FW-based algorithm with a guarantee and a scalable distributed primal-dual FW variant that preserves this guarantee under a differentiable constraint relaxation. The work extends to Gaussian sources and heterogeneous noise, providing unbiased gradient estimators with probabilistic error bounds and extensive simulations on synthetic and backbone topologies showing near-centralized performance. The results demonstrate that multicast-based design substantially improves throughput and model quality, offering practical avenues for edge-enabled distributed learning. Limitations include synchronization requirements, motivating future work on asynchronous schemes and shadow-price-based gradient estimation, along with publicly available code and data.

Abstract

As edge computing capabilities increase, model learning deployments in diverse edge environments have emerged. In experimental design networks, introduced recently, network routing and rate allocation are designed to aid the transfer of data from sensors to heterogeneous learners. We design efficient experimental design network algorithms that are (a) distributed and (b) use multicast transmissions. This setting poses significant challenges as classic decentralization approaches often operate on (strictly) concave objectives under differentiable constraints. In contrast, the problem we study here has a non-convex, continuous DR-submodular objective, while multicast transmissions naturally result in non-differentiable constraints. From a technical standpoint, we propose a distributed Frank-Wolfe and a distributed projected gradient ascent algorithm that, coupled with a relaxation of non-differentiable constraints, yield allocations within a factor from the optimal. Numerical evaluations show that our proposed algorithms outperform competitors with respect to model learning quality.
Paper Structure (19 sections, 12 theorems, 57 equations, 5 figures, 2 tables, 3 algorithms)

This paper contains 19 sections, 12 theorems, 57 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Centralized Algorithm
  5. DR-submodularity
  6. Algorithm Overview
  7. Gradient Estimation
  8. Distributed Algorithm
  9. Algorithm Overview
  10. Distributed FW Implementation Details
  11. Projected Gradient Ascent
  12. Numerical Evaluation
  13. Experimental Setup
  14. Performance Metrics
  15. Results
  16. ...and 4 more sections

Key Result

Theorem 1

Objective $U (\boldsymbol{\lambda})$ is (a) monotone-increasing and (b) continuous DR-submodular with respect to $\boldsymbol{\lambda}$. Moreover, the partial derivative of $U$ is: where $t\xspace = t\xspace^{\ell\xspace}$, $\ell\xspace$ is the last node of $p\xspace$, the distribution $\mathrm{P}$ is Poisson described by eq:Poisson prod, with parameters governed by $\lambda_{s\xspace}^{\ell\xspa

Figures (5)

  • Figure 1: An experimental design networkliu2022experimental. Sources (yellow) generate streams of data from diverse sensors, e.g., cameras, microphones, seismic sensors, etc. Learners (blue) train distinct models over (possibly overlapping) received data. We wish to allocate bandwidth to data traffic in a manner that maximizes the social welfare, i.e., the aggregate quality of models across learners.
  • Figure 2: Aggregate utility, infeasibility and estimation error across networks. DFW and DPGA perform very well in terms of maximizing the utility and minimizing the estimation error in all networks. The aggregate utilities of DFW and DPGA are also listed in Tab. \ref{['tab:topologies']}. Furthermore, their performances are close to their centralized versions: FW and PGA, with an acceptable infeasibility $\sim 0.1$.
  • Figure 3: Stepsize effect on primal dual gradient algorithms over topology ER. Larger stepsizes lead to better performance, and DFW and DPGA are always the best in terms of both utility and estimation error. However, stepsizes above $0.03$ lead to numerical instability.
  • Figure 4: Varying source rates and source set size over GEANT. When increasing source rates and source set sizes, learners receive more data. This leads to higher aggregate utility, and lower estimation error. Our algorithms, DFW and DPGA, stay close to their centralized versions (FW and PGA) and outperform competitors in both metrics, with a small change in feasibility.
  • Figure 5: Varying learner set size over topology SW. The aggregate utility increases, while the estimation error remains essentially unchanged, as the number of learners increases. DFW and DPGA again stay close to their centralized versions and outperform competitors.

Theorems & Definitions (20)

  • Definition 1: DR-Submodularity bian2017guaranteedsoma2015generalization
  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Theorem 3
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • proof
  • ...and 10 more