Stochastic approximation method using diagonal positive-definite matrices for convex optimization with fixed point constraints
Open Access
- 12 April 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Fixed Point Theory and Algorithms for Sciences and Engineering
- Vol. 2021 (1), 1-31
- https://doi.org/10.1186/s13663-021-00695-3
Abstract
This paper proposes a stochastic approximation method for solving a convex stochastic optimization problem over the fixed point set of a quasinonexpansive mapping. The proposed method is based on the existing adaptive learning rate optimization algorithms that use certain diagonal positive-definite matrices for training deep neural networks. This paper includes convergence analyses and convergence rate analyses for the proposed method under specific assumptions. Results show that any accumulation point of the sequence generated by the method with diminishing step-sizes almost surely belongs to the solution set of a stochastic optimization problem in deep learning. Additionally, we apply the learning methods based on the existing and proposed methods to classifier ensemble problems and conduct a numerical performance comparison showing that the proposed learning methods achieve high accuracies faster than the existing learning method.Keywords
Funding Information
- Japan Society for the Promotion of Science London (JP18K11184)
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