From Oja's Algorithm to the Multiplicative Weights Update Method with Applications
Optimization and Control
2023-10-25 v1 Machine Learning
Abstract
Oja's algorithm is a well known online algorithm studied mainly in the context of stochastic principal component analysis. We make a simple observation, yet to the best of our knowledge a novel one, that when applied to a any (not necessarily stochastic) sequence of symmetric matrices which share common eigenvectors, the regret of Oja's algorithm could be directly bounded in terms of the regret of the well known multiplicative weights update method for the problem of prediction with expert advice. Several applications to optimization with quadratic forms over the unit sphere in are discussed.
Cite
@article{arxiv.2310.15559,
title = {From Oja's Algorithm to the Multiplicative Weights Update Method with Applications},
author = {Dan Garber},
journal= {arXiv preprint arXiv:2310.15559},
year = {2023}
}