We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a smoothened sliced OT (SOT) plan. To the best of our knowledge, SROT is the first approach to leverage a version of SOT plan as a reference to improve classical OT. We provide a formal definition of SROT, derive its dual formulation, and provide a post-Bayesian interpretation of SROT. We then develop a Sinkhorn-style algorithm for efficient computation, retaining the same scalability advantages as EOT. By incorporating a scalable SOT plan as a prior, SROT yields more accurate approximations of the exact OT plan than EOT under the same level of regularization. Moreover, the resulting transport plan improves upon the reference SOT plan itself. We further introduce the corresponding OT divergence induced by SROT, named SROT divergence, and analyze its topological and computational properties. Finally, we validate our approach through experiments on synthetic datasets and color transfer tasks, demonstrating that SROT is better than both EOT and SOT in approximating exact OT. Additional experiments on gradient flows further highlight the advantages of SROT divergence.

翻译：我们提出了一种新的正则化最优传输（OT）框架，称为切片正则化最优传输（SROT）。与通过向独立耦合施加正则化项的熵正则化OT（EOT）不同，SROT将传输计划正则化至光滑切片OT（SOT）计划。据我们所知，SROT是首个利用SOT计划作为参考来改进经典OT的方法。我们给出了SROT的形式化定义，推导了其对偶形式，并提供了SROT的贝叶斯后验解释。随后，我们开发了一种Sinkhorn风格的算法以实现高效计算，保留了与EOT相同的可扩展性优势。通过引入可扩展的SOT计划作为先验，SROT在相同正则化水平下能更精确地逼近真实OT计划。此外，所得的传输计划本身优于参考SOT计划。我们进一步引入了由SROT诱导的对应OT散度，称为SROT散度，并分析了其拓扑与计算性质。最后，我们在合成数据集和颜色迁移任务上验证了该方法，结果表明SROT在逼近真实OT方面优于EOT和SOT。附加的梯度流实验进一步凸显了SROT散度的优势。