Sliced-Regularized Optimal Transport
A new approach uses sliced OT as a reference for better transport plans.
Khai Nguyen introduces Sliced-Regularized Optimal Transport (SROT), a novel regularization approach for optimal transport (OT) that diverges from the standard entropic OT (EOT) paradigm. While EOT regularizes the transport plan toward an independent coupling, SROT instead uses a smoothened sliced OT (SOT) plan as a reference. This is the first method to leverage a version of SOT in this way, providing a formal definition, dual formulation, and a post-Bayesian interpretation. Nguyen also develops a Sinkhorn-style algorithm that retains EOT's scalability while yielding more accurate approximations of the exact OT plan under the same regularization level.
Experimental validation on synthetic datasets and color transfer tasks shows SROT outperforms both EOT and SOT in approximating exact OT. The resulting transport plan improves upon the reference SOT plan itself. Additionally, the SROT divergence is introduced, with analysis of its topological and computational properties. Further experiments on gradient flows highlight additional advantages, suggesting SROT could become a new standard for tasks requiring precise transport, such as domain adaptation or image generation.
- SROT uses a smoothened sliced OT plan as a reference instead of an independent coupling, improving accuracy.
- A Sinkhorn-style algorithm is provided, maintaining scalability comparable to entropic OT.
- Outperforms both EOT and SOT in synthetic tests, color transfer, and gradient flow experiments.
Why It Matters
SROT offers a more accurate, scalable alternative to entropic OT, potentially improving ML tasks like domain adaptation and image generation.