Online Distributed Convex Optimization on Dynamic Networks

Hosseini, Saghar; Chapman, Airlie; Mesbahi, Mehran

doi:10.1109/tac.2016.2525928

Cited by 148 publications

(81 citation statements)

References 35 publications

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“…On the other hand, the work [10] extended the distributed dual averaging algorithm in [2] to online setting, and derived an O(1/ √ T ) average regret rate. The authors in [11] further applied the online distributed dual averaging algorithm to dynamic networks. The authors in [12] proposed an online distributed optimization that is based on mirror descent and established its convergence analysis results.…”

Section: Introductionmentioning

confidence: 99%

Distributed Mirror Descent for Online Composite Optimization

Yuan

et al. 2021

IEEE Trans. Automat. Contr.

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In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss function that changes over time and a regularization function. This problem naturally arises in many real-world applications ranging from wireless sensor networks to signal processing. We propose a class of online distributed optimization algorithms that are based on approximate mirror descent, which utilize the Bregman divergence as distance-measuring function that includes the Euclidean distances as a special case. We consider two standard information feedback models when designing the algorithms, that is, full-information feedback and bandit feedback. For the full-information feedback model, the first algorithm attains an average regularized regret of order O(1/ √ T ) with the total number of rounds T . The second algorithm, which only requires the information of the values of the loss function at two predicted points instead of the gradient information, achieves the same average regularized regret as that of the first algorithm. Simulation results of a distributed online regularized linear regression problem are provided to illustrate the performance of the proposed algorithms.Index Terms-Online distributed optimization, composite objective, average regularized regret, approximate mirror descent, bandit feedback.

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Section: Introductionmentioning

confidence: 99%

Distributed Mirror Descent for Online Composite Optimization

Yuan

et al. 2021

IEEE Trans. Automat. Contr.

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“…The work in [16] extends these results to zeroth-order methods. Unconstrained distributed online gradient descent algorithms are studied in [17]- [20]. These distributed methods deal with unconstrained problems and still achieve sublinear regret rates provided the stepsizes are chosen appropriately and the network of agents is connected.…”

Section: Introductionmentioning

confidence: 99%

A Distributed Online Convex Optimization Algorithm with Improved Dynamic Regret

Zhang

Ravier

Zavlanos

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We consider the problem of distributed online convex optimization, where a group of agents collaborate to track the trajectory of the global minimizers of sums of time-varying objective functions in an online manner. For general convex functions, the theoretical upper bounds of existing methods are given in terms of regularity measures associated with the dynamical system as well as the time horizon. It is thus of interest to determine whether the explicit time horizon dependence can be removed as in the case of centralized optimization. In this work, we propose a novel distributed online gradient descent algorithm and show that the dynamic regret bound of this algorithm has no explicit dependence on the time horizon. Instead, it depends on a new regularity measure quantifying the total change in gradients at the optimal points at each time. The main driving force of our algorithm is an online adaptation of the gradient tracking technique used in static optimization. Since, in many applications, time-varying objective functions and the corresponding optimal points follow a non-adversarial dynamical system, we also consider the role of prediction assuming that the optimal points evolve according to a linear dynamical system. We present numerical experiments that show that our proposed algorithm outperforms the existing distributed mirror descentbased state of the art methods in term of the optimizer tracking performance. We also present an empirical example suggesting that the analysis of our algorithm is optimal in the sense that the regularity measures in the theoretical bounds cannot be removed.

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“…In the OCO literature, a benchmark to evaluate a strategy is provided by the regret [29,19,36,18,23,21,28], which basically measures the difference between the player's sequence of decisions and the best strategy in hindsight (i.e., the minimization of each f t ). A strategy is defined successful if its regret is sublinear in T .…”

Section: Introductionmentioning

confidence: 99%

“…This result was improved in [23], which obtained O(1 + C T ), where C T is the sum of the distances between successive reference points. Very recently, regret has been investigated also in OCO distributed settings [21,28].…”

Section: Introductionmentioning

confidence: 99%

Online Optimization in Dynamic Environments: A Regret Analysis for Sparse Problems

Fosson

2018

2018 IEEE Conference on Decision and Control (CDC)

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Time-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this paper, we consider this problem in the context of the sparse optimization; specifically, we consider the Elastic-net model, which promotes parsimonious solutions. Following the rationale in [23], we propose an online algorithm and we theoretically prove that it is successful in terms of dynamic regret. We then show an application to the problem of recursive identification of time-varying autoregressive models, in the case when the number of parameters to be estimated is unknown. Numerical results show the practical efficiency of the proposed method.

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Online Distributed Convex Optimization on Dynamic Networks

Cited by 148 publications

References 35 publications

Distributed Mirror Descent for Online Composite Optimization

Distributed Mirror Descent for Online Composite Optimization

A Distributed Online Convex Optimization Algorithm with Improved Dynamic Regret

Online Optimization in Dynamic Environments: A Regret Analysis for Sparse Problems

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