Discrete Probabilistic Inverse Optimal Transport
This work addresses a foundational gap in optimal transport theory, but it appears incremental as it builds on existing entropy-regularized OT methods.
The paper tackles the problem of inferring the cost matrix in inverse optimal transport, which is less understood than optimal transport, by formalizing and analyzing its properties using entropy-regularized OT tools, with results including theoretical characterizations and empirical simulations.
Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well understood than OT. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples and simulations validating theoretical results.