This academic article explores the Partial Optimal Transport (POT) problem – a mathematical problem concerning the transportation of unbalanced measures or quantities. The authors critique the current state-of-the-art Sinkhorn algorithm for POT, citing its incompatibility and poor performance in practical applications. In response, the authors propose a new rounding algorithm for POT and provide a feasible Sinkhorn procedure with a revised computation complexity. The study also introduces two first-order methods to approximate the POT problem: Adaptive Primal-Dual Accelerated Gradient Descent and Dual Extrapolation. The authors demonstrate the flexibility of POT compared to standard Optimal Transport and the practicality of the new algorithms in real-world applications.
Publication date: 22 Dec 2023
Project Page: Not provided
Paper: https://arxiv.org/pdf/2312.13970
