Stability and Performance Limits of Adaptive Primal-Dual Networks

Towfic, Zaid J.; Sayed, Ali H.

doi:10.1109/tsp.2015.2415759

Cited by 46 publications

(44 citation statements)

References 56 publications

(101 reference statements)

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“…Several useful strategies have been proposed to solve constrained and unconstrained versions of this problem in a fully decentralized manner [1]- [13]. Diffusion strategies [3], [8]- [12] are attractive since they are scalable, robust, and enable continuous learning and adaptation in response to drifts in the location of the minimizer due to changes in the costs or in the constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The technique relies on combining diffusion adaptation with a stochastic gradient projection step, and on the use of constant step-sizes to enable continuous adaptation and learning from streaming data. Since we are learning from streaming data, the dual function cannot be computed exactly and the use of primal-dual methods may result in stability problems as already shown in [12]. For this reason, we focus on primal techniques.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion LMS for Multitask Problems With Local Linear Equality Constraints

Nassif

Richard

Ferrari

et al. 2017

IEEE Trans. Signal Process.

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We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set of linear equality constraints. Each agent possesses its own convex cost function of its parameter vector and a set of linear equality constraints involving its own parameter vector and the parameter vectors of its neighboring agents. We propose an adaptive stochastic algorithm based on the projection gradient method and diffusion strategies in order to allow the network to optimize the individual costs subject to all constraints. Although the derivation is carried out for linear equality constraints, the technique can be applied to other forms of convex constraints. We conduct a detailed mean-square-error analysis of the proposed algorithm and derive closed-form expressions to predict its learning behavior. We provide simulations to illustrate the theoretical findings. Finally, the algorithm is employed for solving two problems in a distributed manner: a minimum-cost flow problem over a network and a space-time varying field reconstruction problem.subject to ∈Ip D p w + b p = 0, p = 1, . . . , P. (1b) Each agent k in the network seeks to estimate its own M k × 1 parameter vector w k , and has knowledge of its cost function J k (·) and the set of linear equality constraints that agent k is involved in. Each constraint is indexed by p, and defined by the L p × M matrices D p , the L p × 1 vector b p , and the set

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffusion LMS for Multitask Problems With Local Linear Equality Constraints

Nassif

Richard

Ferrari

et al. 2017

IEEE Trans. Signal Process.

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“…The combination matrices A are chosen using the Metropolis rule (66). We see that the coupled diffusion algorithm outperforms its ADMM counterpart even though the ADMM uses global information in step (116), which indicates that primal-dual methods do not necessarily perform well under adaptive networks as shown in [47]. We also notice that the smaller the step-size is, the smaller is the steady-state MSD, and, moreover, the closer the coupled diffusion becomes to the centralized.…”

Section: A Unconstrained Casementioning

confidence: 93%

Distributed Coupled Multiagent Stochastic Optimization

Alghunaim

Sayed

2020

IEEE Trans. Automat. Contr.

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This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of the entries of a global parameter vector or model, and is subject to convex constraints that are only known locally. Problems of this type arise in several applications, most notably in disease propagation models, minimum-cost flow problems, distributed control formulations, and distributed power system monitoring. This work focuses on stochastic settings, where a stochastic risk function is associated with each agent and the objective is to seek the minimizer of the aggregate sum of all risks subject to a set of constraints. Agents are not aware of the statistical distribution of the data and, therefore, can only rely on stochastic approximations in their learning strategies. We derive an effective distributed learning strategy that is able to track drifts in the underlying parameter model. A detailed performance and stability analysis is carried out showing that the resulting coupled diffusion strategy converges at a linear rate to an O(µ)−neighborhood of the true penalized optimizer.

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“…III. ASYNCHRONOUS SADDLE POINT METHOD Methods based upon distributed gradient descent and penalty methods more generally [28]- [30] are inapplicable to settings with nonlinear constraints, with the exception of [31], which requires attenuating learning rates to attain constraint satisfaction. On the other hand, the dual methods proposed in [32]- [34] require a nonlinear minimization computation at each algorithm iteration, and thus is impractically costly.…”

Section: Remarkmentioning

confidence: 99%

Asynchronous Saddle Point Algorithm for Stochastic Optimization in Heterogeneous Networks

Bedi

Koppel

Rajawat

2019

IEEE Trans. Signal Process.

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We consider expected risk minimization in multi-agent systems comprised of distinct subsets of agents operating without a common time-scale. Each individual in the network is charged with minimizing the global objective function, which is an average of sum of the statistical average loss function of each agent in the network. Since agents are not assumed to observe data from identical distributions, the hypothesis that all agents seek a common action is violated, and thus the hypothesis upon which consensus constraints are formulated is violated. Thus, we consider nonlinear network proximity constraints which incentivize nearby nodes to make decisions which are close to one another but not necessarily coincide. Moreover, agents are not assumed to receive their sequentially arriving observations on a common time index, and thus seek to learn in an asynchronous manner. An asynchronous stochastic variant of the Arrow-Hurwicz saddle point method is proposed to solve this problem which operates by alternating primal stochastic descent steps and Lagrange multiplier updates which penalize the discrepancies between agents. This tool leads to an implementation that allows for each agent to operate asynchronously with local information only and message passing with neighbors. Our main result establishes that the proposed method yields convergence in expectation both in terms of the primal sub-optimality and constraint violation to radii of sizes O( √ T ) and O(T 3/4 ), respectively. Empirical evaluation on an asynchronously operating wireless network that manages user channel interference through an adaptive communications pricing mechanism demonstrates that our theoretical results translates well to practice.

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Stability and Performance Limits of Adaptive Primal-Dual Networks

Cited by 46 publications

References 56 publications

Diffusion LMS for Multitask Problems With Local Linear Equality Constraints

Diffusion LMS for Multitask Problems With Local Linear Equality Constraints

Distributed Coupled Multiagent Stochastic Optimization

Asynchronous Saddle Point Algorithm for Stochastic Optimization in Heterogeneous Networks

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