A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport
| Source: Apple ML Research
Tags: optimal transport, Apple ML Research, kernel methods, AISTATS, computational ML, MIT, Berkeley
Apple ML Research and MIT/Berkeley researchers propose a semismooth Newton method for kernel-based optimal transport that achieves local quadratic convergence, substantially cutting the computational cost that previously made these estimators intractable at scale.
Details
Kernel-based optimal transport (OT) estimators are statistically superior to plug-in methods for comparing probability distributions in high dimensions, but their reliance on the short-step interior-point method (SSIPM) made them computationally prohibitive as sample size n grows. This paper, published at AISTATS 2026 by Tianyi Lin (MIT), Marco Cuturi, and Michael I. Jordan (Berkeley) in collaboration with Apple ML Research, directly attacks that bottleneck. The key contribution is a nonsmooth fixed-point reformulation of the kernel-based OT problem that can be solved efficiently with a specialized semismooth Newton (SSN) method. By exploiting the problem structure, the per-iteration cost of each SSN step is substantially reduced in practice. The method achieves O(1/√k) global convergence and local quadratic convergence under standard regularity conditions. Experiments on both synthetic and real datasets show substantial speedups over SSIPM, potentially bringing kernel OT estimators into practical reach for the sample sizes common in modern ML pipelines. This is a clean algorithmic contribution with no product or licensing angle — value is for researchers and practitioners working on distribution comparison, domain adaptation, or generative modeling.