2000 character limit reached
Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes (2211.10420v3)
Published 18 Nov 2022 in cs.LG and stat.ML
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.