A note on overrelaxation in the Sinkhorn algorithm

TL;DR

This paper provides a theoretical framework for overrelaxation in the Sinkhorn algorithm, establishing parameter ranges that ensure convergence and improve speed, along with a zero-cost method for near-optimal parameter selection.

Contribution

It introduces an a priori parameter range for overrelaxation in the Sinkhorn algorithm and a spectral analysis-based zero-cost method for near-optimal parameter choice.

Findings

Guaranteed global convergence with overrelaxation.

Faster asymptotic local convergence.

Zero-cost near-optimal parameter selection method.

Abstract

We derive an a priori parameter range for overrelaxation of the Sinkhorn algorithm, which guarantees global convergence and a strictly faster asymptotic local convergence. Guided by the spectral analysis of the linearized problem we pursue a zero cost procedure to choose a near optimal relaxation parameter.