Transient performance analysis of adaptive multitask network based on correntropy criterion

Abstract

In this paper, we investigate the transient performance of the proposed distributed multitask learning algorithm that is developed based on maximum correntropy criterion. In the first stage, we derive the proposed multitask learning algorithm in which the correntropy-based combination matrix determines which sensors should collaborate together and which sensors should stop the collaboration. In the second stage, according to the variance relation of the error vector, we derive a closed-form relation that shows the transition of mean-square-deviation learning performance. We also find the lower and upper bounds of the step size that ensure the stability of the multitask learning algorithm. The theoretical finding of the transient performance is shown to fit a well match with simulation results. KEYWORDS adaptive network, correntropy criterion, distributed signal processing, multitask learning, transient analysis Int J Adapt Control Signal Process. 2018;32:229-247.wileyonlinelibrary.com/journal/acs

Decentralized Decision-Making Over Multi-Task Networks

“…From (14) agents that share the same desired model will have identical columns in matrix Y k i , namely, if agents m and ℓ have the same desired model at time instant i, this implies that:…”

“…After updating matrix Y k i and generating the local labels {l k ℓ (i)}, agent k counts how many models are desired by its neighborhood to update C k (i). In the example (14), agent k distinguishes at time instant i three desired models {2, 24, 37}, i.e., C k (i) = 3. Agent k labels these three different models locally as: {2, 24, 37}.…”

“…An analogy would be a school of fish tracking a food source: all elements in the fish school sense distance and direction to the same food source and are interested in approaching it. On the other hand, multi-task networks [9,10,11,12,13,14,15,16,17] involve agents sensing data arising from different models and different clusters of agents may be interested in identifying separate models. A second analogy is a school of fish sensing information about multiple food sources.…”

Transient analysis of multitask learning over adaptive networks with wireless links

“…[2][3][4][5][6][7][8][9][10][11] Adaptive networks are split into multi-task and single-task networks. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In a single-task network, there is one target vector to estimate; however, in a multi-task network, multiple target vectors should be estimated. [11][12][13][14][15][16][17] The links in the topology of adaptive networks can be connected through wireless or wired links.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In a single-task network, there is one target vector to estimate; however, in a multi-task network, multiple target vectors should be estimated. [11][12][13][14][15][16][17] The links in the topology of adaptive networks can be connected through wireless or wired links. In References 18-23 the learning performance of distributed algorithms for single-task networks with noisy wired link, and in References 24-28, the learning performance of distributed algorithms for single-task networks with wireless fading links were studied.…”