  Acceleration for non-convex functions has been an important problem in
optimisation. We revisit star-convex functions, which are strictly unimodal on
all lines through a minimizer. In [1], the authors accelerate gradient descent
for star-convex functions with gradients that are Lipschitz with respect to the
Euclidean norm in an unconstrained domain. In this paper, we introduce a new
assumption about the regularity of the derivative of a general norm and we
accelerate mirror descent for this class of normed spaces. We show that, under
it, our algorithms show sharp convergence rates for star-convex functions with
-H"older continuous gradients. We also prove that our convergence rate is near
optimal for -norms.
  [1] Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond,
Hinder Oliver and Sidford Aaron and Sohoni Nimit
