2016

Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems

Schmitzer, Bernhard

Understand

Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport.

  • However, a standard implementation of the scaling algorithm has several numerical limitations: the scaling factors diverge and convergence becomes impractically slow as the entropy regularization approaches zero.
  • Moreover, handling the dense kernel matrix becomes unfeasible for large problems.
  • To address this, we combine several modifications: A log-domain stabilized formulation, the well-known epsilon-scaling heuristic, an adaptive truncation of the kernel and a coarse-to-fine scheme.

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