Efficient Second Order Online Learning by Sketching
This work addresses computational bottlenecks in online learning for practitioners dealing with high-dimensional or sparse data, representing an incremental improvement over existing methods.
The paper tackles the computational inefficiency of second-order online learning methods for ill-conditioned data by proposing Sketched Online Newton (SON), which achieves linear time complexity in dimension and sparsity, eliminating previous computational obstacles.
We propose Sketched Online Newton (SON), an online second order learning algorithm that enjoys substantially improved regret guarantees for ill-conditioned data. SON is an enhanced version of the Online Newton Step, which, via sketching techniques enjoys a running time linear in the dimension and sketch size. We further develop sparse forms of the sketching methods (such as Oja's rule), making the computation linear in the sparsity of features. Together, the algorithm eliminates all computational obstacles in previous second order online learning approaches.