Meta Optimal Transport

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 focus on Meta OT for entropic OT problems between discrete measures where we predict approximations of the optimal duals that can be fine-tuned with the Sinkhorn algorithm. Our experiments demonstrate that Meta OT is capable of predicting rapid initializations for transport problems between 1) MNIST digits, 2) spherical data, and 3) classification labels for CIFAR-10, CIFAR-100, and Fashion MNIST.