Kernel Neural Optimal Transport

Alexander Korotin; Daniil Selikhanovych; Evgeny Burnaev

Kernel Neural Optimal Transport

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arxiv 2205.15269 v2 pith:H2AQP32D submitted 2022-05-30 cs.LG stat.ML

Alexander Korotin , Daniil Selikhanovych , Evgeny Burnaev This is my paper · ORCID

classification cs.LGstat.ML

keywords optimaltransportkernelcostsneuralplansquadraticweak

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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.

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