Distributed Stochastic Optimization via Correlated Scheduling

Neely, Michael J.

doi:10.1109/tnet.2014.2382597

Cited by 19 publications

(32 citation statements)

References 20 publications

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“…In medium access control problem [9], users set their individual channel access probability to maximize their benefit. In wireless sensor networks, sensor nodes collect information to serve a fusion center, an interesting problem is to make each node independently decide the quality of its report to maximize the average quality of information gathered by the fusion center subject to some power constraint [10], [11], note that a higher level of quality requires higher power consumption. This paper considers an optimization problem in a distributed network where each node adjusts its own action to maximize the global utility of the system, which is also perturbed by a stochastic process, e.g., wireless channels.…”

Section: Introductionmentioning

confidence: 99%

Distributed stochastic optimization in networks with low informational exchange

Assaad

Duhamel

2017

2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes. Gradient descent method is a common technique to solve the optimization problem, while the computation of the gradient may require much information exchange. In this paper, we consider that each node can only have a noisy numerical observation of its local utility, of which the closed-form expression is not available. This assumption is quite realistic, especially when the system is too complicated or constantly changing. Nodes may exchange the observation of their local utilities to estimate the global utility at each timeslot. We propose stochastic perturbation based distributed algorithms under the assumptions whether each node has collected local utilities of all or only part of the other nodes. We use tools from stochastic approximation to prove that both algorithms converge to the optimum. The convergence rate of the algorithms is also derived. Although the proposed algorithms can be applied to general optimization problems, we perform simulations considering power control in wireless networks and present numerical results to corroborate our claim.

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Section: Introductionmentioning

confidence: 99%

Distributed stochastic optimization in networks with low informational exchange

Assaad

Duhamel

2017

2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…S TOCHASTIC optimization algorithms have been extensively studied over decades and can be traced back to the epochal work [22], which have been widely employed in different areas, e.g., machine learning [23]- [25], [52], [53], power systems [51], wireless communication [5]- [7], and bioinformatics [50]. In particular, the classical stochastic approximation (SA) of the exact gradient, also known as stochastic gradient descent (SGD), has been widely applied to these stochastic optimization problems, where the gradient information is employed in finding the search direction.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization With Applications

Chen

Chan

et al. 2020

IEEE Trans. Neural Netw. Learning Syst.

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Ensuring the positive definiteness and avoiding illconditioning of the Hessian update in the stochastic Broyden-Fletcher-Goldfarb-Shanno (BFGS) method are significant in solving nonconvex problems. This paper proposes a novel stochastic version of damped and regularized BFGS method for addressing the above problems. While the proposed regularized strategy helps to prevent the BFGS matrix from being close to singularity, the new damped parameter further ensures positivity of the product of correction pairs. To alleviate the computational cost of the stochastic LBFGS updates, and to improve its robustness, the curvature information is updated using the averaged iterate at spaced intervals. The effectiveness of the proposed method is evaluated through the logistic regression and Bayesian logistic regression problems in machine learning. Numerical experiments are conducted by using both synthetic dataset and several real datasets. The results show that the proposed method generally outperforms the stochastic damped limited memory BFGS (SdLBFGS) method. In particular, for problems with small sample sizes, our method has shown superior performance and is capable of mitigating ill-conditioned problems. Furthermore, our method is more robust to the variations of the batch size and memory size than the SdLBFGS method.Index Terms-nonconvex optimization, stochastic quasi-Newton method, LBFGS, damped parameter, nonconjugate exponential models, variational inference.

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“…This calls for a distributed version of the DPP algorithm with theoretical guarantees. The author in [4] considers a relaxed version of the above problem. In particular, assuming i.i.d.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, assuming i.i.d. states with correlated "common information," the author in [4] proposes a distributed DPP algorithm, and proves that the approximate distributed DPP algorithm is close to being optimal. Several authors use the above results in various contexts such as crowd sensing [17], energy efficient scheduling in MIMO systems [18], to name a few.…”

Section: Introductionmentioning

confidence: 99%

“…However, in many practical applications, the states evolve in a dependent and non-stationary fashion [13]. Thus, the following assumptions about the state made in [4] need to be relaxed: (i) independent and (ii) identically distributed. Further, from practical and theoretical standpoints, it is important to investigate the rate of convergence of the distributed algorithm to the optimal.…”

Section: Introductionmentioning

confidence: 99%

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Time complexity analysis of distributed stochastic optimization in a non-stationary environment

Bharath

Vaishali

2017

2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

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In this paper, we consider a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of related stochastic processes called penalties. We assume that the state of the system is evolving in an independent and non-stationary fashion and the "common information" available at each node is distributed and delayed. Such stochastic optimization is an integral part of many important problems in wireless networks such as scheduling, routing, resource allocation and crowd sensing. We propose an approximate distributed Drift-Plus-Penalty (DPP) algorithm, and show that it achieves a time average cost (and penalties) that is within ǫ > 0 of the optimal cost (and constraints) with high probability. Also, we provide a condition on the convergence time t for this result to hold. In particular, for any delay D ≥ 0 in the common information, we use a coupling argument to prove that the proposed algorithm converges almost surely to the optimal solution. We use an application from wireless sensor network to corroborate our theoretical findings through simulation results.

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Distributed Stochastic Optimization via Correlated Scheduling

Cited by 19 publications

References 20 publications

Distributed stochastic optimization in networks with low informational exchange

Distributed stochastic optimization in networks with low informational exchange

A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization With Applications

Time complexity analysis of distributed stochastic optimization in a non-stationary environment

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