Dynamical Schrodinger Bridge Problems on Graphs

Authors：Chow, Shui-Nee; Li, Wuchen^*; Mou, Chenchen; Zhou, Haomin

Source：Journal of Dynamics and Differential Equations, 2022, 34(3): 2511-2530.

DOI：10.1007/s10884-021-09977-1

• Optimal transport
• Schrodinger bridge problem
• Fisher information
• Hamiltonian system
• Graph

We study a discrete dynamical Schrodinger bridge problem (SBP) as a dynamical variational problem on a finite graph. We prove that the discrete SBP exists a unique minimizer, which satisfies a boundary value Hamiltonian flow on probability simplex equipped with L-2-Wasserstein metric. In our formulation, we establish the connection between discrete SBP problems and Hamiltonian flows.