Simplifying Optimal Transport through Schatten-$p$ Regularization

TMLR Paper6193 Authors

Abstract: We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional structure. The convexity of our formulation enables direct theoretical analysis: we derive optimality conditions and prove recovery guarantees for low-rank couplings and barycentric maps in simplified settings. To efficiently solve the proposed program, we develop a mirror-descent algorithm with convergence guarantees for $p \geq 1$. Experiments on synthetic and real data demonstrate the method’s efficiency, scalability, and ability to recover low-rank transport structures.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Ju_Sun1

Submission Number: 6193