Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes

TL;DR

Mirror Sinkhorn introduces a fast, noise-robust online optimization algorithm for convex objectives on transport polytopes, combining Sinkhorn scaling and mirror descent principles, with proven guarantees and practical effectiveness.

Contribution

It presents a novel single-loop algorithm that efficiently optimizes convex functions on transport polytopes in an online setting, integrating Sinkhorn and mirror descent methods.

Findings

Algorithm is robust to noise.

Effective on synthetic and real-world data.

Provides theoretical guarantees.

Abstract

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.