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