Optimal stochastic second-order optimization for unconstrained convex problems

Develop an optimal stochastic second-order method for unconstrained convex optimization over \(\mathbb{R}^d\), extending optimal convergence guarantees beyond bounded convex domains and domain-diameter-dependent rates.

Background

The paper establishes optimal stochastic second-order convergence rates for convex optimization over compact convex sets, where the guarantees depend on the domain diameter $D$. Its Stochastic Contracting Cubic Newton and Accelerated Stochastic Contracting Cubic Newton methods therefore do not resolve the corresponding unconstrained problem over $\mathbb{R}^d$. The authors explicitly identify obtaining an optimal method in that setting as an unresolved problem.