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Varying Infimum Gradient Descent Algorithm for Agent-Sever Systems Using Different Order Iterative Preconditioning Methods
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DOI：10.1109/TII.2021.3123304.png)
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摘要
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In the traditional gradient descent (T-GD) algorithm, the convergence rate is strongly depend on the condition number of the information matrix: a larger condition number leads to a poor optimal convergence factor infimum mu(op), which sets a convergence rate ceiling. That is, once the information matrix is fixed, the convergence factor of the T-GD algorithm reaches at most the infimum mu(op). This article studies a varying infimum gradient descent algorithm, which can move down the infimum by using different order iterative preconditioning methods, as follows: first, for infinite iterative algorithm, the infimum becomes smaller and smaller with the increased iteration numbers; second, for finite iterative algorithm, the infimum is equal to zero, and the parameter estimates can be obtained in only one iteration; third, construct an adaptive interval between zero and mu(op), which can establish a link between the least squares and T-GD algorithms. Based on the varying infimum gradient descent algorithm, researchers can adaptively choose preconditioning matrices for different kinds of models on a case by case basis. The convergence analysis and simulation examples show effectiveness of the proposed algorithms.
Keyword:
Agent-server system
convergence rate
gradient descent (GD) algorithm
preconditioning matrix
varying infimum
期刊
IF:
9.9
论文数:
8.6K
被引数:
6.0W
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