Almost Sure Convergence of Distributed Optimization with Imperfect Information Sharing

Reisizadeh, Hadi; Gokhale, Anand; Touri, Behrouz; Mohajer, Soheil

doi:10.48550/arxiv.2210.05897

Cited by 2 publications

(4 citation statements)

References 18 publications

(36 reference statements)

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“…The above assumption is specific to the imperfect information sharing setup and is also used in [28], [29], [31], [32].…”

Section: B Assumptionsmentioning

confidence: 99%

“…Previous studies have evaluated the effectiveness of two-time scale methods in DFL with noisy channels. However, these investigations were limited by inflexible assumptions such as strong convexity in papers such as [26]- [29]. These assumptions are rarely satisfied in practical and large-scale learning scenarios, which limits the applicability of the proposed methods.…”

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confidence: 99%

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On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

Chellapandi

Upadhyay

Hashemi

et al. 2023

IEEE Control Syst. Lett.

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A novel Decentralized Noisy Model Update Tracking Federated Learning algorithm (FedNMUT) is proposed that is tailored to function efficiently in the presence of noisy communication channels that reflect imperfect information exchange. This algorithm uses gradient tracking to minimize the impact of data heterogeneity while minimizing communication overhead. The proposed algorithm incorporates noise into its parameters to mimic the conditions of noisy communication channels, thereby enabling consensus among clients through a communication graph topology in such challenging environments. FedNMUT prioritizes parameter sharing and noise incorporation to increase the resilience of decentralized learning systems against noisy communications. Theoretical results for the smooth non-convex objective function are provided by us, and it is shown that the ϵ−stationary solution is achieved by our algorithm at the rate of O 1 √ T , where T is the total number of communication rounds. Additionally, via empirical validation, we demonstrated that the performance of FedNMUT is superior to the existing state-of-the-art methods and conventional parameter-mixing approaches in dealing with imperfect information sharing. This proves the capability of the proposed algorithm to counteract the negative effects of communication noise in a decentralized learning framework.Imperfect information exchange, such as noisy or quantized communication, has been examined in the context of average consensus algorithms within distributed frameworks. Yet, the ramifications of varying noise levels remain underexplored. Moreover, existing research, primarily focused on consensus issues, does not fully address the complex challenges encountered in contemporary decentralized optimization and learning paradigms [23], [24]. In contrast to Federated Learning (FL), where server assistance is common, Decentralized Federated Learning (DFL) operates without a central server, with each client acting autonomously, processing local Stochastic Gradient Descent (SGD) or its variants on its data and interacting directly with neighboring clients.In our previous paper [25], we performed a comparative study of three proposed algorithms for DFL under imperfect communication conditions, typified by noisy channels. These algorithms-FedNDL1, FedNDL2, and FedNDL3-differ in their handling of noise and parameter sharing, demonstrating varying degrees of resilience to communication noise. In this paper, we propose a novel algorithm that employs the Gradient Tracking method in DFL and compare its performance against the previously mentioned algorithms. C. Paper's ContributionsThis paper introduces a novel algorithm that employs the Gradient Tracking method in DFL, considering the impact of communication noise. Previous studies have evaluated the effectiveness of two-time scale methods in DFL with noisy channels. However, these investigations were limited by inflexible assumptions such as strong convexity in papers such as [26]- [29]. These assumptions are rarely satisfied in practi...

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“…The above assumption is specific to the imperfect information sharing setup and is also used in [28], [29], [31], [32].…”

Section: B Assumptionsmentioning

confidence: 99%

mentioning

confidence: 99%

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

Chellapandi

Upadhyay

Hashemi

et al. 2023

IEEE Control Syst. Lett.

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show abstract

“…This assumption is specific to the imperfect information sharing setup and is considered recently in [26], [29], [30].…”

Section: Assumptionsmentioning

confidence: 99%

“…In this paper, our primary focus is on DFL in the presence of noise in communication channels. Recently, [27]- [30] study the performance of a two-time scale method [31] for DFL with channel noise while requiring the convexity of the objective function, uniformly bounded gradients, and access to the deterministic gradients; note that these three considerations are very restrictive assumptions, especially in emerging settings in large-scale learning.…”

mentioning

confidence: 99%

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

Chellapandi¹,

Upadhyay²,

Hashemi³

et al. 2023

Preprint

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Decentralized learning and optimization is a central problem in control that encompasses several existing and emerging applications, such as federated learning. While there exists a vast literature on this topic and most methods centered around the celebrated average-consensus paradigm, less attention has been devoted to scenarios where the communication between the agents may be imperfect. To this end, this paper presents three different algorithms of Decentralized Federated Learning (DFL) in the presence of imperfect information sharing modeled as noisy communication channels. The first algorithm, Federated Noisy Decentralized Learning (FedNDL1), comes from the literature, where the noise is added to their parameters to simulate the scenario of the presence of noisy communication channels. This algorithm shares parameters to form a consensus with the clients based on a communication graph topology through a noisy communication channel. The proposed second algorithm ( FedNDL2) is similar to the first algorithm but with added noise to the parameters, and it performs the gossip averaging before the gradient optimization. The proposed third algorithm (FedNDL3), on the other hand, shares the gradients through noisy communication channels instead of the parameters. Theoretical and experimental results demonstrate that under imperfect information sharing, the third scheme that mixes gradients is more robust in the presence of a noisy channel compared with the algorithms from the literature that mix the parameters.

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Almost Sure Convergence of Distributed Optimization with Imperfect Information Sharing

Cited by 2 publications

References 18 publications

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

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