论文标题
关于摊销凸结合物以进行最佳运输
On amortizing convex conjugates for optimal transport
论文作者
论文摘要
本文着重于计算解决Euclidean Wasserstein-2最佳运输问题时产生的凸共轭操作。这种共轭也被称为legendre-fenchel共轭或c传输，被认为很难计算，在实践中，Wasserstein-2方法受到限制，因为他们不能精确地在连续空间中确切结合双重电位。为了克服这一点，可以通过摊销优化近似结合的计算，该优化学会了预测结合物的模型。我表明，将对偶联物与求解器进行微调相结合，可以显着提高Korotin等人在Wasserstein-2基准中学到的传输质量。 （2021a），能够对文献中考虑的许多二维耦合和流进行建模。本文中的所有基线，方法和求解器均可在http://github.com/facebookresearch/w2ot上获得。
This paper focuses on computing the convex conjugate operation that arises when solving Euclidean Wasserstein-2 optimal transport problems. This conjugation, which is also referred to as the Legendre-Fenchel conjugate or c-transform,is considered difficult to compute and in practice,Wasserstein-2 methods are limited by not being able to exactly conjugate the dual potentials in continuous space. To overcome this, the computation of the conjugate can be approximated with amortized optimization, which learns a model to predict the conjugate. I show that combining amortized approximations to the conjugate with a solver for fine-tuning significantly improves the quality of transport maps learned for the Wasserstein-2 benchmark by Korotin et al. (2021a) and is able to model many 2-dimensional couplings and flows considered in the literature. All of the baselines, methods, and solvers in this paper are available at http://github.com/facebookresearch/w2ot.
