Convergence of Constrained Anderson Acceleration

TL;DR

This paper establishes non-asymptotic linear convergence rates for the constrained Anderson acceleration method by deriving new bounds on a constrained Chebyshev problem, with practical computational costs.

Contribution

It introduces convergence guarantees for constrained Anderson acceleration through novel bounds on a constrained polynomial minimization problem.

Findings

Proves non-asymptotic linear convergence rates.

Derives new bounds on the constrained Chebyshev problem.

Maintains computational cost comparable to the original scheme.

Abstract

We prove non asymptotic linear convergence rates for the constrained Anderson acceleration extrapolation scheme. These guarantees come from new upper bounds on the constrained Chebyshev problem, which consists in minimizing the maximum absolute value of a polynomial on a bounded real interval with $l_1$ constraints on its coefficients vector. Constrained Anderson Acceleration has a numerical cost comparable to that of the original scheme.