Abstract: We propose a new formulation and learning strategy for computing the
Wasserstein geodesic between two probability distributions in high dimensions.
By applying the method of Lagrange multipliers to the dynamic formulation of
the optimal transport (OT) problem, we derive a minimax problem whose saddle
point is the Wasserstein geodesic. We then parametrize the functions by deep
neural networks and design a sample based bidirectional learning algorithm for
training. The trained networks enable sampling from the Wasserstein geodesic.
As by-products, the algorithm also computes the Wasserstein distance and OT map
between the marginal distributions. We demonstrate the performance of our
algorithms through a series of experiments with both synthetic and realistic