Distributed Convex Optimization With State-Dependent (Social) Interactions and Time-Varying Topologies

Alaviani, Seyyed Shaho; Elia, Nicola

doi:10.1109/tsp.2021.3070223

Cited by 8 publications

(7 citation statements)

References 74 publications

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“…Let |S i * | ≥ 1 and |S j * | ≥ 1 where S i is given by Eq. (10). Then, according to Load-Balancing algorithm, nodes i * , j * update their states to their average with probability…”

Section: B Proof Of Propositionmentioning

confidence: 99%

See 1 more Smart Citation

Maximal Dissent: a Fast way to Agree in Distributed Convex Optimization

Verma¹,

Vasconcelos²,

Mitra³

et al. 2022

Preprint

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Consider a set of agents collaboratively solving a distributed convex optimization problem, asynchronously, under stringent communication constraints. In such situations, when an agent is activated and is allowed to communicate with only one of its neighbors, we would like to pick the one holding the most informative local estimate. We propose new algorithms where the agents with maximal dissent average their estimates, leading to an information mixing mechanism that often displays faster convergence to an optimal solution compared to randomized gossip. The core idea is that when two neighboring agents whose distance between local estimates is the largest among all neighboring agents in the network average their states, it leads to the largest possible immediate reduction of the quadratic Lyapunov function used to establish convergence to the set of optimal solutions. As a broader contribution, we prove the convergence of max-dissent subgradient methods using a unified framework that can be used for other state-dependent distributed optimization algorithms. Our proof technique bypasses the need of establishing the information flow between any two agents within a time interval of uniform length by intelligently studying convergence properties of the Lyapunov function used in our analysis.

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“…Let |S i * | ≥ 1 and |S j * | ≥ 1 where S i is given by Eq. (10). Then, according to Load-Balancing algorithm, nodes i * , j * update their states to their average with probability…”

Section: B Proof Of Propositionmentioning

confidence: 99%

“…robots, autonomous vehicles, drones, etc.). In such settings, the state-dependency arises from the fact that agents that are physically closer have a higher probability of successfully communicating with each other [9][10][11]. Existing results assume that the local interactions between agents lead to strong connectivity over time.…”

Section: Introductionmentioning

confidence: 99%

Maximal Dissent: a Fast way to Agree in Distributed Convex Optimization

Verma¹,

Vasconcelos²,

Mitra³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The objective is to minimize the sum of local functions by local communication and local computation. Its variants were developed in [17][18][19][20][21][22][23]. Furthermore, Chen et al [24] developed distributed subgradient algorithm for weakly convex functions.…”

Section: Dmentioning

confidence: 99%

“…Duchi et al [17] proposed a distributed dual average method using a similar idea. Moreover, variants of the distributed subgradient algorithm can be also found in [18][19][20][21][22][23][24]. However, the pro-jection step becomes prohibitive when dealing with massive data sets for solving the constrained optimization problem.…”

Section: Introductionmentioning

confidence: 99%

A distributed gradient algorithm based on randomized block-coordinate and projection-free over networks

Zhu

Wang

Zhang

et al. 2022

Complex Intell. Syst.

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The computational bottleneck in distributed optimization methods, which is based on projected gradient descent, is due to the computation of a full gradient vector and projection step. This is a particular problem for large datasets. To reduce the computational complexity of existing methods, we combine the randomized block-coordinate descent and the Frank–Wolfe techniques, and then propose a distributed randomized block-coordinate projection-free algorithm over networks, where each agent randomly chooses a subset of the coordinates of its gradient vector and the projection step is eschewed in favor of a much simpler linear optimization step. Moreover, the convergence performance of the proposed algorithm is also theoretically analyzed. Specifically, we rigorously prove that the proposed algorithm can converge to optimal point at rate of $${\mathcal {O}}(1/t)$$ O ( 1 / t ) under convexity and $${\mathcal {O}}(1/t^2)$$ O ( 1 / t 2 ) under strong convexity, respectively. Here, t is the number of iterations. Furthermore, the proposed algorithm can converge to a stationary point, where the “Frank-Wolfe” gap is equal to zero, at a rate $${\mathcal {O}}(1/\sqrt{t})$$ O ( 1 / t ) under non-convexity. To evaluate the computational benefit of the proposed algorithm, we use the proposed algorithm to solve the multiclass classification problems by simulation experiments on two datasets, i.e., aloi and news20. The results shows that the proposed algorithm is faster than the existing distributed optimization algorithms due to its lower computation per iteration. Furthermore, the results also show that well-connected graphs or smaller graphs leads to faster convergence rate, which can confirm the theoretical results.

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“…Based on the analysis of the spectrum and eigenvector of the system, the work [17] proposes a unifying framework for reaching arithmetic, geometric and harmonic average consensus, where the communication network is undirected and modulated by distance. A distributed convex optimization problem has been studied in [18] for a state-dependent undirected multiagent network. In [19], mean square consensus has been tackled for a multiagent system with white noises using event-trigged strategies.…”

Section: Introductionmentioning

confidence: 99%

Constrained Consensus in State-Dependent Directed Multiagent Networks

Shang

2022

IEEE Trans. Netw. Sci. Eng.

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In this paper, constrained consensus of a group of continuous-time dynamical agents over state-dependent networks is investigated. The communication network, modulated by an asymmetric distance between agents, accommodates general directed information flows. Each agent proposes a comfortable range in a distributed manner, where they are inclined to agree on the final equilibrium state. Based on Lyapunov stability theory and robustness analysis, different conditions have been obtained to guarantee convergence within the common comfortable range when the network connectivity is fixed and time-varying. No global information is required in the proposed nonlinear control protocols. Furthermore, an opinion dynamics model has been introduced incorporating both social observer effect and bounded confidence phenomenon in the same state-dependent framework. Relaxed consensus conditions have been derived under certain symmetric assumptions. Finally, numerical examples have been presented to verify the effectiveness of the theoretical results.

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Distributed Convex Optimization With State-Dependent (Social) Interactions and Time-Varying Topologies

Cited by 8 publications

References 74 publications

Maximal Dissent: a Fast way to Agree in Distributed Convex Optimization

Maximal Dissent: a Fast way to Agree in Distributed Convex Optimization

A distributed gradient algorithm based on randomized block-coordinate and projection-free over networks

Constrained Consensus in State-Dependent Directed Multiagent Networks

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