Online Adaptive Principal Component Analysis and Its extensions

TL;DR

This paper introduces online adaptive PCA algorithms with sub-linear regret guarantees, capable of adjusting to changing environments, advancing beyond static regret measures.

Contribution

It presents novel online adaptive PCA algorithms with theoretical and experimental validation, focusing on adaptive regret in dynamic settings.

Findings

Algorithms achieve sub-linear adaptive regret.

They effectively adapt to changing environments.

Experimental results confirm theoretical guarantees.

Abstract

We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the underlying environment is changing. Instead, we adopt the adaptive regret metric from the previous literature and propose online adaptive algorithms for PCA and variance minimization, that have sub-linear adaptive regret guarantees. We demonstrate both theoretically and experimentally that the proposed algorithms can adapt to the changing environments.