Online Adaptive Principal Component Analysis and Its extensions
This work addresses the need for adaptive methods in online PCA for dynamic environments, representing an incremental improvement over static regret approaches.
The authors tackled the problem of online principal component analysis (PCA) and variance minimization in changing environments by proposing algorithms with sub-linear adaptive regret guarantees, demonstrating both theoretically and experimentally that these algorithms can adapt effectively.
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.