Smooth and Sparse Optimal Transport

Understand

Entropic regularization is quickly emerging as a new standard in optimal transport (OT).

• It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the Sinkhorn algorithm.
• However, entropy keeps the transportation plan strictly positive and therefore completely dense, unlike unregularized OT.
• This lack of sparsity can be problematic in applications where the transportation plan itself is of interest.