Stochastic Subgradient Algorithms for Strongly Convex Optimization Over Distributed Networks

Sayin, Muhammed O.; Vanli, N. Denizcan; Kozat, Süleyman S.; Başar, Tamer

doi:10.1109/tnse.2017.2713396

Cited by 46 publications

(11 citation statements)

References 33 publications

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“…Distributed algorithms dealing with problem (1) have been studied extensively in the literature [56,36,37,28,19,20,52,13,46,34,45]. Recently, there has been considerable interest in distributed implementation of stochastic gradient algorithms [48,54,14,3,5,55,6,9,10,7,32,24,26,40,51,41,18]. The literature has shown that distributed methods may compete with, or even outperform, their centralized counterparts under certain conditions [9,10,26,40,41].…”

Section: Scenarios In Which Problemmentioning

confidence: 99%

Distributed stochastic gradient tracking methods

2020

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In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size n, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.

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Section: Scenarios In Which Problemmentioning

confidence: 99%

Distributed stochastic gradient tracking methods

2020

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“…Step 2 of the algorithm is known as gossip method, see e.g., [5]), which was initially introduced as an approach for the networks with the imposed connection between the nodes changing by time. We also refer to [30] for similar algorithms in the context of distributed stochastic first-order gradient methods.…”

Section: The Problemmentioning

confidence: 99%

Distributed Zero-Order Optimization under Adversarial Noise

Akhavan,

Pontil,

Tsybakov

2021

Preprint

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We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a distributed zero-order projected gradient descent algorithm to solve this problem. Exchange of information within the network is permitted only between neighbouring nodes. A key feature of the algorithm is that it can query only function values, subject to a general noise model, that does not require zero mean or independent errors. We derive upper bounds for the average cumulative regret and optimization error of the algorithm which highlight the role played by a network connectivity parameter, the number of variables, the noise level, the strong convexity parameter of the global objective and certain smoothness properties of the local objectives. When the bound is specified to the standard undistributed setting, we obtain an improvement over the state-of-the-art bounds, due to the novel gradient estimation procedure proposed here. We also comment on lower bounds and observe that the dependency over certain function parameters in the bound is nearly optimal.

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“…In this work, we focus on the diffusion Kalman filtering as it has been shown that the diffusion-based solutions exhibit superior tracking and stability performance. A successful diffusion implementation requires a connected network and a collaboration mechanism in which, only the agents from a predefined neighborhood are allowed to exchange information with each other [15]- [20]. In this framework, the information is collected by all the agents, which use a local adaptive algorithm, and are scattered through an online sharing mechanism that ripples through the network frequently.…”

Section: Introductionmentioning

confidence: 99%

Energy-Efficient Diffusion Kalman Filtering for Multiagent Networks in IoT

Khalili¹,

Vahidpour²,

Rastegarnia³

et al. 2022

IEEE Internet Things J.

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Increasing the energy efficiency of an Internet of Things (IoT) system is a major challenge for its successful implementation. To reduce the computation and storage burden and enhance the efficiency of traditional IoT, an energy-efficient diffusion-based algorithm for state estimation in multi-agent networks is proposed in this paper. In the proposed algorithm (referred to as reduced-link diffusion Kalman filter (RL-diffKF)) the nodes (agents) can communicate only with a fraction of their neighbors and each node runs a local Kalman filter to estimate the state of a linear dynamic system. This algorithm results in a significant reduction in communication cost during both adaptation and aggregation processes albeit at the expense of possible degradation in the network performance. To justify the stability and convergence of the RL-diffKF algorithm, an indepth analysis of the performance is reported. We also consider the problem of optimal selection of combination weights and use the idea of minimum variance estimation to analytically derive the adaptive combiners. The theoretical findings are verified through numerical simulations.

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Stochastic Subgradient Algorithms for Strongly Convex Optimization Over Distributed Networks

Cited by 46 publications

References 33 publications

Distributed stochastic gradient tracking methods

Distributed stochastic gradient tracking methods

Distributed Zero-Order Optimization under Adversarial Noise

Energy-Efficient Diffusion Kalman Filtering for Multiagent Networks in IoT

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