Distributed Online Learning over Time-varying Graphs via Proximal Gradient Descent

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

doi:10.1109/cdc40024.2019.9029852

Cited by 5 publications

(5 citation statements)

References 26 publications

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“…Remark 3. Recent studies on distributed online convex optimization have shown that the upper bound on the dynamic regret can be as tight as O(1 + C T + V T ) or O(log T (1 + C T )) when the loss functions are strongly convex and smooth (Zhang et al, 2020;Dixit et al, 2019). Theorem 3 shows that by employing multiple consensus averaging iterations over both local decisions and local gradients, DOMD-MADGC can improve the dynamic regret bound to O(1+C T ).…”

Section: Improved Dynamic Regretmentioning

confidence: 96%

“…A distributed online gradient tracking algorithm is proposed in (Lu et al, 2019), which has a dynamic regret bound of O( √ 1 + C T T 3/4 √ ln T ). The dynamic regret of distributed online proximal gradient descent with an O(log t) communication steps per round is bounded by O(log T (1 + C T )) (Dixit et al, 2019). Using the gradient variation as the regularity measure (Li et al, 2020), which is improved to O(1 + C T + V ′ T ) in (Zhang et al, 2020), where V ′ T is a variant of V T in which gradients are evaluated at the optimal points.…”

Section: Related Workmentioning

confidence: 99%

“…Distributed optimization can be more challenging since the learners have only partial information about the global problem, which necessitates engagement in communication so that they can complement their insufficient knowledge. None of the previously proposed distributed online convex optimization algorithms (Shahrampour and Jadbabaie, 2018;Dixit et al, 2019;Zhang et al, 2020) achieve…”

Section: Introductionmentioning

confidence: 99%

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Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

Eshraghi¹,

Liang²

2021

Preprint

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We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a distributed manner. We propose a novel algorithm, termed Distributed Online Mirror Descent with Multiple Averaging Decision and Gradient Consensus (DOMD-MADGC), which is based on mirror descent but incorporates multiple consensus averaging iterations over local gradients as well as local decisions. The key idea is to allow the local learners to collect a sufficient amount of global information, which enables them to more accurately approximation the time-varying global loss, so that they can closely track the dynamic global minimizer over time. We show that the dynamic regret of DOMD-MADGC is upper bounded by the path length, which is defined as the cumulative distance between successive minimizers. The resulting bound improves upon the bounds of existing distributed online algorithms and removes the explicit dependence on T .

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Section: Improved Dynamic Regretmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

Eshraghi¹,

Liang²

2021

Preprint

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“…). [26] considered time-varying network structures and showed that distributed proximal OGD achieves a dynamic regret of O(log T (1 + C * T )) for strongly convex functions. [27] developed a method based on gradient tracking and derived a regret bound in terms of C * T and a gradient pathlength.…”

Section: B Contributionsmentioning

confidence: 99%

On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Chang

Shahrampour

2021

AAAI

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The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence (V_T) and/or the path-length of the minimizer sequence after T rounds. For strongly convex and smooth functions, Zhang et al. (2017) establish the squared path-length of the minimizer sequence (C*_{2,T}) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. We first show that a preconditioned variant of OGD achieves O(min{C*_T,C*_{2,T}}) with one gradient query per round (C*_T refers to the normal path-length). We then propose online optimistic Newton (OON) method for the case when the first and second order information of the function sequence is predictable. The regret bound of OON is captured via the quartic path-length of the minimizer sequence (C*_{4,T}), which can be much smaller than C*_{2,T}. We finally show that by using multiple gradients for OGD, we can achieve an upper bound of O(min{C*_{2,T},V_T}) on regret.

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“…Additional dynamic regret bounds have also been derived for centralized OCO, e.g., Mokhtari et al (2016); Zhang et al (2017a); Besbes et al (2015). In distributed implementation, several recent works have proposed methods that provide dynamic regret guarantee under various assumptions on the convexity and smoothness of the objective functions (Shahrampour and Jadbabaie (2018); Zhang et al (2019); Dixit et al (2019); Lu et al (2020); Sharma et al (2020); Eshraghi and Liang (2020); ; Li et al (2021)). To the best of our knowledge, for gradient/projection-based distributed OCO, the tightest known dynamic regret bound for general convex cost functions is O( T (1 + P T )) (Shahrampour and Jadbabaie (2018)).…”

Section: Dynamic Regret Of Gradient-based and Projection-based Ocomentioning

confidence: 99%

Gradient and Projection Free Distributed Online Min-Max Resource Optimization

Wang¹,

Liang²

2021

Preprint

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We consider distributed online min-max resource allocation with a set of parallel agents and a parameter server. Our goal is to minimize the pointwise maximum over a set of time-varying convex and decreasing cost functions, without a priori information about these functions. We propose a novel online algorithm, termed Distributed Online resource Re-Allocation (DORA), where nonstragglers learn to relinquish resource and share resource with stragglers. A notable feature of DORA is that it does not require gradient calculation or projection operation, unlike most existing online optimization strategies. This allows it to substantially reduce the computation overhead in large-scale and distributed networks. We show that the dynamic regret of the proposed algorithm is upper bounded by O T, where T is the total number of rounds and P T is the path-length of the instantaneous minimizers. We further consider an application to the bandwidth allocation problem in distributed online machine learning. Our numerical study demonstrates the efficacy of the proposed solution and its performance advantage over gradient-and/or projectionbased resource allocation algorithms in reducing wall-clock time.

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Distributed Online Learning over Time-varying Graphs via Proximal Gradient Descent

Cited by 5 publications

References 26 publications

Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Gradient and Projection Free Distributed Online Min-Max Resource Optimization

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