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Accelerated Mirror Descent for Non-Euclidean Star-convex Functions by Lezane, Clement; Langer, Sophie; Koolen, Wouter M is a scholarly article available to read on EtoBox.

What is Accelerated Mirror Descent for Non-Euclidean Star-convex Functions about?

Acceleration for non-convex functions is a fundamental challenge in optimisation. We revisit star-convex functions, which are strictly unimodal on all lines through a minimizer. [1] accelerate unconstrained star-convex minimization of functions that are smooth with respect to the Euclidean norm. To do so, they add a certain binary search step to gradient descent. In this paper, we accelerate unconstrained star-convex minimization of functions that are weakly smooth with respect to an arbitrary norm. We add a binary search step to mirror descent, generalize the approach and refine its complexity analysis. We prove that our algorithms have sharp convergence rates for star-convex functions with $\alpha$-Holder continuous gradients and demonstrate that our rates are nearly optimal for $p$-norms. [1] Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond, Hinder Oliver and Sidford Aaron and Sohoni Nimit

Author

Lezane, Clement; Langer, Sophie; Koolen, Wouter M

Published

2024

Language

EN