🤖 AI Summary
This work addresses the challenge in partial optimal transport (POT) where only a fraction of mass needs to be transported due to mismatched marginal distributions or the presence of outliers. While existing Sinkhorn-based methods suffer from high computational complexity and limited scalability, we propose an accelerated Sinkhorn algorithm for POT (ASPOT) that, for the first time, integrates Nesterov-type acceleration into the Sinkhorn framework. By combining alternating minimization with entropy regularization, ASPOT reduces the computational complexity to $\mathcal{O}(n^{7/3} \varepsilon^{-5/3})$. Furthermore, we introduce an optimized strategy for selecting the entropy regularization parameter to enhance convergence rates. Both theoretical analysis and experiments on real-world scenarios demonstrate the superior efficiency and performance of ASPOT compared to existing approaches.
📝 Abstract
Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are widely used, their complexity bounds for POT remain suboptimal and can limit scalability. We introduce Accelerated Sinkhorn for POT (ASPOT), which integrates alternating minimization with Nesterov-style acceleration in the POT setting, yielding a complexity of $\mathcal{O}(n^{7/3}\varepsilon^{-5/3})$. We also show that an informed choice of the entropic parameter $\gamma$ improves rates for the classical Sinkhorn method. Experiments on real-world applications validate our theories and demonstrate the favorable performance of our proposed methods.