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In this paper, we present the first stepsize schedule for Newton methodresulting in fast global and local convergence guarantees. In particular, a) weprove an $O\left( \frac 1 {k^2} \right)$ global rate, which matches thestate-of-the-art global rate of cubically regularized Newton method of Polyakand Nesterov (2006) and of regularized Newton method of Mishchenko (2021) andDoikov and Nesterov (2021), b) we prove a local quadratic rate, which matchesthe best-known local rate of second-order methods, and c) our stepsize formulais simple, explicit, and does not require solving any subproblem. Ourconvergence proofs hold under affine-invariance assumptions closely related tothe notion of self-concordance. Finally, our method has competitive performancewhen compared to existing baselines, which share the same fast globalconvergence guarantees.

A Damped Newton Method Achieves Global $O\left(\frac{1}{k^2}\right)$ and Local Quadratic Convergence Rate