Kernel Neural Optimal Transport
This work addresses a specific problem in optimal transport algorithms for researchers in machine learning, offering an incremental improvement to enhance reliability in applications like image translation.
The paper tackled the issue of Neural Optimal Transport (NOT) learning suboptimal transport plans with weak quadratic costs by introducing kernel weak quadratic costs, which improved theoretical guarantees and practical performance, achieving competitive results on unpaired image-to-image translation tasks.
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To resolve this issue, we introduce kernel weak quadratic costs. We show that they provide improved theoretical guarantees and practical performance. We test NOT with kernel costs on the unpaired image-to-image translation task.