arXiv 2602.022412026-02cs.LG

变分熵最优传输

Variational Entropic Optimal Transport

Lomonosov Moscow State University（莫斯科罗蒙诺索夫莫斯科大学）；National Research Nuclear University MEPhI（国家研究核大学 MEPhI）

Roman Dyachenko, Nikita Gushchin, Kirill Sokolov, Petr Mokrov, Evgeny Burnaev, Alexander Korotin

AI总结：

本文提出变分熵最优传输（VarEOT），通过精确的变分重参数化将对数分区函数转化为可处理的最小化问题，从而在不依赖MCMC模拟的情况下实现高效的最优传输学习，理论上有有限样本泛化界和通用函数逼近结果，并在合成数据和未配对图像到图像翻译任务中展示了竞争力或改进的翻译质量。

摘要：

熵最优传输（EOT）在连续空间中以二次成本为经典工具，用于解决领域迁移问题。在实践中，最近的方法优化一个弱对偶EOT目标，依赖于单一势能函数，但这样做在计算上效率不高，因为对数分区项不可计算。现有方法通常通过两种方式解决这一障碍：通过显著限制传输家族以获得闭式归一化（通过高斯混合参数化），或通过使用通用神经参数化，需要基于模拟的训练过程。我们提出变分熵最优传输（VarEOT），基于对数分区$\log \mathbb{E}[\exp(\cdot)]$的精确变分重参数化，作为对辅助对数归一化进行可处理的最小化。这产生了一个可微学习目标，通过随机梯度优化，并避免了训练期间MCMC模拟的必要性。我们提供了理论保证，包括有限样本泛化界和在通用函数逼近下的近似结果。在合成数据和未配对图像到图像翻译实验中，展示了竞争力或改进的翻译质量，而与使用相同弱对偶EOT目标的求解器比较支持所提出优化原理的优势。我们的求解器代码可在https://github.com/DrEternity/VarEOT找到。

英文摘要：

Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but doing so is computationally not efficient due to the intractable log-partition term. Existing methods typically resolve this obstacle in one of two ways: by significantly restricting the transport family to obtain closed-form normalization (via Gaussian-mixture parameterizations), or by using general neural parameterizations that require simulation-based training procedures. We propose Variational Entropic Optimal Transport (VarEOT), based on an exact variational reformulation of the log-partition $\log \mathbb{E}[\exp(\cdot)]$ as a tractable minimization over an auxiliary log-normalizer. This yields a differentiable learning objective optimized with stochastic gradients and avoids the necessity of MCMC simulations during the training. We provide theoretical guarantees, including finite-sample generalization bounds and approximation results under universal function approximation. Experiments on synthetic data and unpaired image-to-image translation demonstrate competitive or improved translation quality, while comparisons within the solvers that use the same weak dual EOT objective support the benefit of the proposed optimization principle. The code for our solver can be found at https://github.com/DrEternity/VarEOT .

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文