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In this paper, we propose the first sketch-and-project Newton method withfast $\mathcal O(k^{-2})$ global convergence rate for self-concordantfunctions. Our method, SGN, can be viewed in three ways: i) as asketch-and-project algorithm projecting updates of Newton method, ii) as acubically regularized Newton ethod in sketched subspaces, and iii) as a dampedNewton method in sketched subspaces. SGN inherits best of all three worlds:cheap iteration costs of sketch-and-project methods, state-of-the-art $\mathcalO(k^{-2})$ global convergence rate of full-rank Newton-like methods and thealgorithm simplicity of damped Newton methods. Finally, we demonstrate itscomparable empirical performance to baseline algorithms.

Sketch-and-Project Meets Newton Method: Global $\mathcal O(k^{-2})$ Convergence with Low-Rank Updates