Light Unbalanced Optimal Transport
CoRR(2023)
摘要
While the continuous Entropic Optimal Transport (EOT) field has been actively
developing in recent years, it became evident that the classic EOT problem is
prone to different issues like the sensitivity to outliers and imbalance of
classes in the source and target measures. This fact inspired the development
of solvers that deal with the unbalanced EOT (UEOT) problem - the
generalization of EOT allowing for mitigating the mentioned issues by relaxing
the marginal constraints. Surprisingly, it turns out that the existing solvers
are either based on heuristic principles or heavy-weighted with complex
optimization objectives involving several neural networks. We address this
challenge and propose a novel theoretically-justified, lightweight, unbalanced
EOT solver. Our advancement consists of developing a novel view on the
optimization of the UEOT problem yielding tractable and a non-minimax
optimization objective. We show that combined with a light parametrization
recently proposed in the field our objective leads to a fast, simple, and
effective solver which allows solving the continuous UEOT problem in minutes on
CPU. We prove that our solver provides a universal approximation of UEOT
solutions and obtain its generalization bounds. We give illustrative examples
of the solver's performance.
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关键词
transport,optimal
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