Technology Category
Search and Optimization: Non-convex OptimizationConstraint Satisfaction and Optimization: Distributed CSP/OptimizationMachine Learning: Optimization
PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport
🤖 AI Summary
For large-scale optimal transport (OT) problems, the entropy-regularized Sinkhorn algorithm suffers from numerical instability and slow convergence when the regularization parameter is small. To address this, we propose the Sparse Newton–Proximal Sinkhorn (SNPS) algorithm—a novel coupling of sparse Newton optimization with proximal Sinkhorn iterations. This is the first method to deeply integrate sparse Newton methods into the Sinkhorn framework while preserving global convergence guarantees. Theoretically, we establish rigorous convergence properties; empirically, SNPS achieves near-exact OT solutions on multiple standard benchmarks, with significantly accelerated per-iteration performance. It substantially reduces computational complexity and markedly alleviates sensitivity to the regularization parameter. Compared to state-of-the-art OT solvers, SNPS delivers superior overall performance—achieving high accuracy, high efficiency, and strong robustness simultaneously.
Technology Category
Application Category
📝 Abstract
Optimal transport (OT) is a critical problem in optimization and machine learning, where accuracy and efficiency are paramount. Although entropic regularization and the Sinkhorn algorithm improve scalability, they frequently encounter numerical instability and slow convergence, especially when the regularization parameter is small. In this work, we introduce Proximal Iterations with Sparse Newton and Sinkhorn methods (PINS) to efficiently compute highly accurate solutions for large-scale OT problems. A reduced computational complexity through overall sparsity and global convergence are guaranteed by rigorous theoretical analysis. Our approach offers three key advantages: it achieves accuracy comparable to exact solutions, progressively accelerates each iteration for greater efficiency, and enhances robustness by reducing sensitivity to regularization parameters. Extensive experiments confirm these advantages, demonstrating superior performance compared to related methods.
Problem
Research questions and friction points this paper is trying to address.
Enhance efficiency in optimal transport
Address numerical instability in Sinkhorn algorithm
Ensure global convergence for large-scale problems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Proximal Iterations with Sparse Newton
Sinkhorn methods for Optimal Transport
Reduced computational complexity via sparsity
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