Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes
This work addresses the need for efficient and robust optimization methods in machine learning applications involving optimal transport, though it appears incremental as it builds on existing Sinkhorn and mirror descent techniques.
The paper tackles the problem of optimizing convex objectives on transport polytopes by introducing a single-loop algorithm that combines Sinkhorn scaling and mirror descent, achieving robustness to noise and applicability in online settings, with experimental validation on synthetic and real-world data.
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.