Meta Optimal Transport
This work addresses computational inefficiency in optimal transport for applications like image processing and data analysis, though it appears incremental as it builds on existing OT methods with amortized optimization.
The authors tackled the problem of repeatedly solving similar optimal transport (OT) problems by introducing Meta OT, which uses amortized optimization to predict OT maps from input measures, leveraging past solutions to speed up new computations. This approach improved computational time compared to standard methods that solve each problem from scratch.
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot