Optimal Resource Allocation for Detection of a Gaussian Process Using a MAC in WSNs

135

114

We consider a distributed learning problem over multiple access channel (MAC) using a large wireless network. The computation is made by the network edge and is based on received data from a large number of distributed nodes which transmit over a noisy fading MAC. The objective function is a sum of the nodes' local loss functions. This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms and the network edge receives a superposition of the analog transmitted signals used for updating the estimate. GBMA does not require power control or beamforming to cancel the fading effect as in other algorithms, and operates directly with noisy distorted gradients. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks. Specifically, we establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. Furthermore, we provide energy scaling laws for approaching the centralized convergence rate as the number of nodes increases. Finally, experimental results support the theoretical findings, and demonstrate strong performance of GBMA using synthetic and real data.Tomer Sery is with the

Section: Related Workmentioning

confidence: 99%

“…and(34) with h n,k = 1,σ 2 h = 0 we can write the term E [ ∇F (θ k ), θ k+1 − θ k ] as E ∇F (θ k ) T (−βv k ) = −βE ∇F (θ k ) T (∇F (θ k ) + w k ) = −βE ||∇F (θ k )|| −βE ||v k || 2 + β dσ…”

mentioning

confidence: 99%

On Analog Gradient Descent Learning Over Multiple Access Fading Channels

Sery

Cohen

2020

135

114

“…observation case, which make the problem fundamentally different. Other related works have investigated MAC for detection in WSN using multiple antennas at the FC [38], detection with a non-linear sensing behavior [39], and detecting a stationary random process distributed in space and time with a circularlysymmetric complex Gaussian distribution [40], [41]. However, these studies are fundamentally different from the settings considered in this paper.…”

Section: B Related Workmentioning

confidence: 99%

Spectrum and Energy Efficient Multiple Access for Detection in Wireless Sensor Networks

Cohen

Leshem

2018

We consider a binary hypothesis testing problem using Wireless Sensor Networks (WSNs). The decision is made by a fusion center and is based on received data from the sensors. We focus on a spectrum and energy efficient transmission scheme used to reduce the spectrum usage and energy consumption during the detection task. We propose a Spectrum and Energy Efficient Multiple Access (SEEMA) transmission protocol that performs a censoring-type transmission based on the density of observations using multiple access channels (MAC). Specifically, in SEEMA, only sensors with highly informative observations transmit their data in each data collection. The sensors transmit a common shaping waveform and the fusion center receives a superposition of the analog transmitted signals. SEEMA has important advantages for detection tasks in WSNs. First, it is highly energy and bandwidth efficient due to transmission savings and narrowband transmission over MAC. Second, it can be implemented by simple dumb sensors (oblivious to observation statistics, and local data processing is not required) which simplifies the implementation as compared to existing MAC transmission schemes for detection in WSNs. We establish a finite sample analysis and an asymptotic analysis of the error probability with respect to the network size and provide system design conditions to obtain the exponential decay of the error. Specific performance analysis is developed for common noni.i.d. observation scenarios, including local i.i.d. observations, and Markovian correlated observations. Numerical examples demonstrate SEEMA performance.

“…is the estimation distortion given by (12), and Q m := blkdiag{Q k,m } K k=1 . Note that (P1) cannot be decomposed in time since sensor energy constraints are temporally inseparable.…”

Section: Moreover the Transmission Cost (6) Can Be Rewritten Asmentioning

confidence: 99%

“…where G k has been introduced in the paragraph that proceeds (12). Combining (15) and (16), we can rewrite the estimation error covariance as a function of the collaboration vector…”

Section: B Collaboration Problem For the Estimation Of Correlated Pamentioning

confidence: 99%

Optimized Sensor Collaboration for Estimation of Temporally Correlated Parameters

Liu

Kar

Fardad

et al. 2016

Abstract-In this paper, we aim to design the optimal sensor collaboration strategy for the estimation of time-varying parameters, where collaboration refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. We begin by addressing the sensor collaboration problem for the estimation of uncorrelated parameters. We show that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the nonconvexity. This specific problem structure enables the use of a convexconcave procedure to obtain a near-optimal solution. When the parameters of interest are temporally correlated, a penalized version of the convex-concave procedure becomes well suited for designing the optimal collaboration scheme. In order to improve computational efficiency, we further propose a fast algorithm that scales gracefully with problem size via the alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approach and the impact of parameter correlation and temporal dynamics of sensor networks on estimation performance.