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Related Experiment Video

Updated: Jan 19, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Efficient Implementation of Second-Order Stochastic Approximation Algorithms in High-Dimensional Problems.

Jingyi Zhu, Long Wang, James C Spall

IEEE Transactions on Neural Networks and Learning Systems

|September 20, 2019

Summary

This summary is machine-generated.

This study introduces an efficient method for second-order stochastic approximation algorithms, reducing computational cost from O(p^3) to O(p^2) for high-dimensional problems. This enhances performance in machine learning and optimization tasks.

Related Experiment Videos

Last Updated: Jan 19, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

Optimization Algorithms
Machine Learning Theory
Numerical Analysis

Background:

Stochastic approximation (SA) algorithms are crucial for minimization problems with noisy function evaluations.
Second-order simultaneous perturbation stochastic approximation (2SPSA) and second-order stochastic gradient (2SG) are efficient for high-dimensional problems.
Standard 2SPSA/2SG algorithms have a high per-iteration computational cost of O(p^3) due to matrix operations.

Purpose of the Study:

To develop an efficient implementation technique for 2SPSA/2SG algorithms.
To reduce the per-iteration floating-point-operations (FLOPs) cost of these algorithms.
To maintain the convergence properties of the standard 2SPSA/2SG methods.

Main Methods:

Implementation of 2SPSA/2SG algorithms using symmetric indefinite matrix factorization.
Analysis of the computational complexity reduction.
Verification of convergence properties and numerical stability.

Main Results:

The proposed technique reduces the FLOPs cost from O(p^3) to O(p^2).
The new approach inherits the formal almost sure convergence and rate of convergence from standard 2SPSA/2SG.
Numerical studies demonstrate improved efficiency and stability.

Conclusions:

The symmetric indefinite matrix factorization provides a computationally efficient and numerically stable method for implementing 2SPSA/2SG algorithms.
This advancement is significant for tackling high-dimensional optimization problems in machine learning and other fields.
The method maintains theoretical convergence guarantees while improving practical performance.