Consensus-based Distributed Total Least-squares Estimation Using Parametric Semidefinite Programming

Gratton, Cristiano; Venkategowda, Naveen K. D.; Arablouei, Reza; Werner, Stefan

doi:10.1109/icassp.2019.8682190

Cited by 5 publications

(4 citation statements)

References 28 publications

(46 reference statements)

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“…They both established the performance results under independent signal assumptions. Some other related papers, e.g., [6], [10], [11], verified the efficiency of the LS-type algorithms via numerical simulations. All of these indicate that to substantially relax the widely imposed independence and stationarity conditions on the system signals in the analyses of distributed LS, will inevitably bring challenging difficulties in establishing a convergence theory.…”

Section: Introductionmentioning

confidence: 85%

“…For example, the proposed incremental [3]- [6], consensus [7]- [16], and diffusion [17]- [29] strategies, may be combined with different estimation algorithms, e.g., least mean squares (LMS), LS and Kalman filters (KF) [30]- [33], to give rise to different distributed estimation algorithms. Stability and performance analyses have also been established for different distributed estimation algorithms, for example, incremental LMS [3], [4], consensus LMS [7], [8], diffusion LMS [17]- [22], incremental LS [5], [6], consensus LS [9]- [11], diffusion LS [23]- [29], and distributed KF [12]- [16]. In our recent work (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, almost all the existing studies on the distributed LS (see e.g., [5], [6], [9]- [11], [23]- [29]) require some independent, stationary, or Gaussian assumptions for the system signals. For examples, an incremental LS estimation strategy was proposed in [5], and the mean-square performance was studied for independent regressors.…”

Section: Introductionmentioning

confidence: 99%

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Convergence of a Distributed Least Squares

Xie,

Zhang,

Guo

2019

Preprint

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With the fast development of the sensor and network technology, distributed estimation has attracted more and more attention, due to its capability in securing communication, in sustaining scalability, and in enhancing safety and privacy. In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is allowed to communicate with its neighbors. Our main task is to generalize the well-known theoretical results on the traditional LS to the current distributed case by establishing both the upper bound of the accumulated regrets of the adaptive predictor and the convergence of the distributed LS estimator, with the following key features compared with the existing literature on distributed estimation: Firstly, our theory does not need the previously imposed independence, stationarity or Gaussian property on the system signals, and hence is applicable to stochastic systems with feedback control. Secondly, the cooperative excitation condition introduced and used in this paper for the convergence of the distributed LS estimate is the weakest possible one, which shows that even if any individual sensor cannot estimate the unknown parameter by the traditional LS, the whole network can still fulfill the estimation task by the distributed LS. Moreover, our theoretical analysis is also different from the existing ones for distributed LS, because it is an integration of several powerful techniques including stochastic Lyapunov functions, martingale convergence theorems, and some inequalities on convex combination of nonnegative definite matrices.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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Convergence of a Distributed Least Squares

Xie,

Zhang,

Guo

2019

Preprint

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“…In this context, each agent in the network only possesses information of a local cost function and the agents aim to collaboratively minimize the sum of the local objective functions. Such optimization problems are relevant to several applications in statistics [3]- [5], signal processing [6]- [8] and control [1], [2].…”

Section: Introductionmentioning

confidence: 99%

Distributed Learning with Non-Smooth Objective Functions

Gratton

Venkategowda

Arablouei

et al. 2021

2020 28th European Signal Processing Conference (EUSIPCO)

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We develop a new distributed algorithm to solve a learning problem with non-smooth objective functions when data are distributed over a multi-agent network. We employ a zerothorder method to minimize the associated augmented Lagrangian in the primal domain using the alternating direction method of multipliers (ADMM) to develop the proposed algorithm, named distributed zeroth-order based ADMM (D-ZOA). Unlike most existing algorithms for non-smooth optimization, which rely on calculating subgradients or proximal operators, D-ZOA only requires function values to approximate gradients of the objective function. Convergence of D-ZOA to the centralized solution is confirmed via theoretical analysis and simulation results.

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Privacy-Preserved Distributed Learning With Zeroth-Order Optimization

Gratton

Venkategowda

Arablouei

et al. 2022

IEEE Trans.Inform.Forensic Secur.

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We develop a privacy-preserving distributed algorithm to minimize a regularized empirical risk function when the first-order information is not available and data is distributed over a multi-agent network. We employ a zeroth-order method to minimize the associated augmented Lagrangian function in the primal domain using the alternating direction method of multipliers (ADMM). We show that the proposed algorithm, named distributed zeroth-order ADMM (D-ZOA), has intrinsic privacy-preserving properties. Most existing privacy-preserving distributed optimization/estimation algorithms exploit some perturbation mechanism to preserve privacy, which comes at the cost of reduced accuracy. Contrarily, by analyzing the inherent randomness due to the use of a zeroth-order method, we show that D-ZOA is intrinsically endowed with (ϵ, δ)−differential privacy. In addition, we employ the moments accountant method to show that the total privacy leakage of D-ZOA grows sublinearly with the number of ADMM iterations. D-ZOA outperforms the existing differentially-private approaches in terms of accuracy while yielding similar privacy guarantee. We prove that D-ZOA reaches a neighborhood of the optimal solution whose size depends on the privacy parameter. The convergence analysis also reveals a practically important trade-off between privacy and accuracy. Simulation results verify the desirable privacypreserving properties of D-ZOA and its superiority over the stateof-the-art algorithms as well as its network-wide convergence.

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Consensus-based Distributed Total Least-squares Estimation Using Parametric Semidefinite Programming

Cited by 5 publications

References 28 publications

Convergence of a Distributed Least Squares

Convergence of a Distributed Least Squares

Distributed Learning with Non-Smooth Objective Functions

Privacy-Preserved Distributed Learning With Zeroth-Order Optimization

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