Online distributed optimization via dual averaging

Hosseini, Saghar; Chapman, Airlie; Mesbahi, Mehran

doi:10.1109/cdc.2013.6760092

Cited by 96 publications

(92 citation statements)

References 15 publications

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“…Moreover, Rabbat in [16] proposes a decentralized mirror descent for stochastic composite optimization problems and provide guarantees for strongly convex regularizers. Duchi et al [17] study dual averaging for distributed optimization, and the extension of dual averaging to online distributed optimization is considered in [18]. Mateos-Núnez and Cortés [19] consider online optimization using subgradient descent of local functions, where the graph structure is time-varying.…”

Section: Introductionmentioning

confidence: 99%

An online optimization approach for multi-agent tracking of dynamic parameters in the presence of adversarial noise

Shahrampour

Jadbabaie

2017

2017 American Control Conference (ACC)

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This paper addresses tracking of a moving target in a multi-agent network. The target follows a linear dynamics corrupted by an adversarial noise, i.e., the noise is not generated from a statistical distribution. The location of the target at each time induces a global time-varying loss function, and the global loss is a sum of local losses, each of which is associated to one agent. Agents noisy observations could be nonlinear. We formulate this problem as a distributed online optimization where agents communicate with each other to track the minimizer of the global loss. We then propose a decentralized version of the Mirror Descent algorithm and provide the non-asymptotic analysis of the problem. Using the notion of dynamic regret, we measure the performance of our algorithm versus its offline counterpart in the centralized setting. We prove that the bound on dynamic regret scales inversely in the network spectral gap, and it represents the adversarial noise causing deviation with respect to the linear dynamics. Our result subsumes a number of results in the distributed optimization literature. Finally, in a numerical experiment, we verify that our algorithm can be simply implemented for multi-agent tracking with nonlinear observations.

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Section: Introductionmentioning

confidence: 99%

An online optimization approach for multi-agent tracking of dynamic parameters in the presence of adversarial noise

Shahrampour

Jadbabaie

2017

2017 American Control Conference (ACC)

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“…In this section, we obtain sublinear bounds for the regret and constraint violation defined in (8) and (10), respectively. The next proposition proves sublinearly bounded regret in the cost function.…”

Section: Resultsmentioning

confidence: 99%

“…The consensus framework (A) was used in [8], [9], where a variant of the dual-averaging method by Nesterov [10] for online distributed optimization was proposed for undirected networks [8] and for time-invariant digraphs allowing timevarying weights [9]. Other recent work includes [11], [12] that employ the push-sum protocol [13], [14], which allows for time-varying weight-imbalanced digraphs.…”

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confidence: 99%

Distributed primal-dual methods for online constrained optimization

Lee

Zavlanos

2016

2016 American Control Conference (ACC)

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This paper introduces consensus-based primal-dual methods for distributed online optimization where the timevarying system objective function ft(x) is given as the sum of local agents' objective functions, i.e., ft(x) = i fi,t(xi), and the system constraint function g(x) is given as the sum of local agents' constraint functions, i.e., g(x) = i gi(xi) 0. At each stage, each agent commits to an adaptive decision pertaining only to the past and locally available information, and incurs a new cost function reflecting the change in the environment. Our algorithm uses weighted averaging of the iterates for each agent to keep local estimates of the global constraints and dual variables. We show that the algorithm achieves a regret of order O( √ T ) with the time horizon T , in scenarios when the underlying communication topology is time-varying and jointly-connected. The regret is measured in regard to the cost function value as well as the constraint violation. Numerical results for online routing in wireless multi-hop networks with uncertain channel rates are provided to illustrate the performance of the proposed algorithm.

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“…It is worth emphasizing that the objective functions considered in the aforementioned works are time-invariant. However, in many real applications the objective functions change over time, due to the dynamically changing and uncertain nature of the environment, taking the distributed estimation in sensor networks as an example [10]. Online optimization is known as a powerful tool that can deal with time-varying cost functions that satisfy certain properties (see, e.g., [5]- [9]).…”

Section: Introductionmentioning

confidence: 99%

“…In the work [13], the authors developed a distributed autonomous online learning algorithm that is based on computing local subgradients, and they derived an O(ln T /T ) average regret rate for strongly convex cost functions. 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.…”

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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Online distributed optimization via dual averaging

Cited by 96 publications

References 15 publications

An online optimization approach for multi-agent tracking of dynamic parameters in the presence of adversarial noise

An online optimization approach for multi-agent tracking of dynamic parameters in the presence of adversarial noise

Distributed primal-dual methods for online constrained optimization

Distributed Mirror Descent for Online Composite Optimization

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