An Efficient Mini-batch Method via Partial Transportation

Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the mini-batch level but do not exist in the optimal transportation plan between the original measures. To address the misspecified mappings issue, we propose a novel mini-batch method by using partial optimal transport (POT) between mini-batch empirical measures, which we refer to as mini-batch partial optimal transport (m-POT). Leveraging the insight from the partial transportation, we explain the source of misspecified mappings from the m-OT and motivate why limiting the amount of transported masses among mini-batches via POT can alleviate the incorrect mappings. Finally, we carry out extensive experiments on various applications to compare m-POT with m-OT and recently proposed mini-batch method, mini-batch unbalanced optimal transport (m-UOT). We observe that m-POT is better than m-OT deep domain adaptation applications while having comparable performance with m-UOT. On other applications, such as deep generative model, gradient flow, and color transfer, m-POT yields more favorable performance than both m-OT and m-UOT.