Online Learning Over Dynamic Graphs via Distributed Proximal Gradient Algorithm

Dixit, Rishabh; Bedi, Amrit Singh; Rajawat, Ketan

doi:10.1109/tac.2020.3033712

Cited by 23 publications

(9 citation statements)

References 43 publications

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“…In general, the cost function f t can be smooth or nonsmooth, and in order to exploit the fine structure of f t when it is nonsmooth, the cost function can be considered as a sum of two functions, one is smooth and the other is a nonsmooth regularizer, i.e., composite optimization. Such problems can be naturally found in realistic applications involving low-rank, sparsity, monotonicity, and so forth [23], [24]. • DOL with Nonseparable Global Objectives.…”

Section: A Further Discussion On Problem Settingsmentioning

confidence: 99%

A Survey on Distributed Online Optimization and Game

Li¹,

Xie²,

Li³

2022

Preprint

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Decentralized online learning (DOL) has been increasingly researched in the last decade, mostly motivated by its wide applications in sensor networks, commercial buildings, robotics (e.g., decentralized target tracking and formation control), smart grids, deep learning, and so forth. In this problem, there are a network of agents who may be cooperative (i.e., decentralized online optimization) or noncooperative (i.e., online game) through local information exchanges, and the local cost function of each agent is often time-varying in dynamic and even adversarial environments. At each time, a decision must be made by each agent based on historical information at hand without knowing future information on cost functions. Although this problem has been extensively studied in the last decade, a comprehensive survey is lacking. Therefore, this paper provides a thorough overview of DOL from the perspective of problem settings, communication, computation, and performances. In addition, some potential future directions are also discussed in details.

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Section: A Further Discussion On Problem Settingsmentioning

confidence: 99%

A Survey on Distributed Online Optimization and Game

Li¹,

Xie²,

Li³

2022

Preprint

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“…After that, we apply the proposed algorithms to a distributed target tracking problem, which has been widely investigated in literature, e.g., [16], [44]. Finally, we investigate the dynamic sparse signal recovery problem [17] and compare our algorithm with the existing ones.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Amongst the existing distributed online optimization algorithms, the subgradient descent methods gain considerable attention [10]- [13]. More recently, the authors of [14]- [17] developed distributed online algorithms on the basis of primal-dual method, gradient tracking, mirror descent approach, and proximal gradient algorithm, respectively. The authors of [18] further introduced a primaldual mirror descent algorithm to address distributed online problems with time-varying coupled inequality constraints over weight-balanced digraphs.…”

Section: Introductionmentioning

confidence: 99%

“…The intuition of these distributed algorithms is constructing gradient estimators from function values and then substituting them for the true gradient under the assumption of doubly stochastic weight matrices or fixed networks. Though some efforts have been made to extend zeroth-order distributed algorithms to the online setting [11], [15], [17], [18], [39] Our work [12], [28], they can only be applicable to fixed networks.…”

Section: Introductionmentioning

confidence: 99%

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Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

Xiong¹,

Li²,

You³

et al. 2022

Preprint

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This paper studies a distributed online constrained optimization problem over time-varying unbalanced digraphs without explicit subgradients. In sharp contrast to the existing algorithms, we design a novel consensus-based distributed online algorithm with a local randomized zeroth-order oracle and then rescale the oracle by constructing row-stochastic matrices, which aims to address the unbalancedness of time-varying digraphs. Under mild conditions, the average dynamic regret over a time horizon is shown to asymptotically converge at a sublinear rate provided that the accumulated variation grows sublinearly with a specific order. Moreover, the counterpart of the proposed algorithm when subgradients are available is also provided, along with its dynamic regret bound, which reflects that the convergence of our algorithm is essentially not affected by the zeroth-order oracle. Simulations on distributed targets tracking problem and dynamic sparse signal recovery problem in sensor networks are employed to demonstrate the effectiveness of the proposed algorithm.

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“…Different from the classical distributed learning with static loss functions, each node in distributed online learning has a time-varying loss function f t,i , t ∈ {0, … , T}, i ∈ {1, … , n}, with T the time horizon and n the number of learning nodes in the network. Various algorithms have been developed for distributed online learning, [8][9][10][11][12][13][14][15][16] which aims to minimize the sum of local loss functions over time horizon T. For fixed undirected graphs, a distributed online optimization algorithm based on alternating direction method of multipliers is proposed in the work of Akbari et al, 11 and a distributed mirror descent method for distributed online optimization is developed by using the Bregman divergence in projection. 12 For time-varying graphs, a multistep consensus-based distributed proximal online gradient descent algorithm over undirected networks is proposed in the work of Dixit et al 14 Extended from the dual averaging scheme, a distributed online dual averaging algorithm for distributed online constrained optimization over undirected networks is investigated in the work of Hosseini et al 15 A primal-dual algorithm is further developed for distributed online optimization with coupled constraints over balanced graphs.…”

Section: Introductionmentioning

confidence: 99%

Differentially private distributed online learning over time‐varying digraphs via dual averaging

Han

Liu

Lin

et al. 2021

Intl J Robust & Nonlinear

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This article investigates a distributed online learning problem with privacy preservation, in which the learning nodes in a distributed network aims to minimize the sum of local loss functions over time horizon T. Based on the push-sum protocol and the Laplace mechanism, we propose a differentially private distributed dual averaging algorithm for constrained distributed online learning problem over time-varying digraphs. It is shown that the expectation of the regret of our algorithm achieves a sublinear rate of O( √ T). Furthermore, we provide an analysis of differential privacy, which reveals a tradeoff between the accuracy and the privacy level of our algorithm. Finally, numerical examples are presented to validate the effectiveness of the algorithm.

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Online Learning Over Dynamic Graphs via Distributed Proximal Gradient Algorithm

Cited by 23 publications

References 43 publications

A Survey on Distributed Online Optimization and Game

A Survey on Distributed Online Optimization and Game

Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

Differentially private distributed online learning over time‐varying digraphs via dual averaging

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