An inexact Bregman proximal point method and its acceleration version
  for unbalanced optimal transport
Xiang Chen Faqiang Wang Jun Liu Li Cui
The Unbalanced Optimal Transport (UOT) problem plays increasingly important
roles in computational biology, computational imaging and deep learning.
Scaling algorithm is widely used to solve UOT due to its convenience and good
convergence properties. However, this algorithm has lower accuracy for large
regularization parameters, and due to stability issues, small regularization
parameters can easily lead to numerical overflow. We address this challenge by
developing an inexact Bregman proximal point method for solving UOT. This
algorithm approximates the proximal operator using the Scaling algorithm at
each iteration. The algorithm (1) converges to the true solution of UOT, (2)
has theoretical guarantees and robust regularization parameter selection, (3)
mitigates numerical stability issues, and (4) can achieve comparable
computational complexity to the Scaling algorithm in specific practice.
Building upon this, we develop an accelerated version of inexact Bregman
proximal point method for solving UOT by using acceleration techniques of
Bregman proximal point method and provide theoretical guarantees and
experimental validation of convergence and acceleration.