Accelerated Sinkhorn Algorithms for Partial Optimal Transport

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 $γ$ improves rates for the classical Sinkhorn method. Experiments on real-world applications validate our theories and demonstrate the favorable performance of our proposed methods.

Sparse Partial Optimal Transport via Quadratic Regularization

Partial Optimal Transport (POT) has recently emerged as a central tool in various Machine Learning (ML) applications. It lifts the stringent assumption of the conventional Optimal Transport (OT) that input measures are of equal masses, which is often not guaranteed in real-world datasets, and thus offers greater flexibility by permitting transport between unbalanced input measures. Nevertheless, existing major solvers for POT commonly rely on entropic regularization for acceleration and thus return dense transport plans, hindering the adoption of POT in various applications that favor sparsity. In this paper, as an alternative approach to the entropic POT formulation in the literature, we propose a novel formulation of POT with quadratic regularization, hence termed quadratic regularized POT (QPOT), which induces sparsity to the transport plan and consequently facilitates the adoption of POT in many applications with sparsity requirements. Extensive experiments on synthetic and CIFAR-10 datasets, as well as real-world applications such as color transfer and domain adaptations, consistently demonstrate the improved sparsity and favorable performance of our proposed QPOT formulation.