On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint

• Published in: Journal of optimization theory and applications Vol. 169; no. 2; pp. 671 - 691
• Main Authors: Chen, Yongxin, Georgiou, Tryphon T., Pavon, Michele
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2016; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Computational fluid dynamics; Differential equations; Engineering; Joints; Mathematical analysis; Mathematics; Mathematics and Statistics; Noise; Operations Research/Decision Theory; Optimal control; Optimization; Partial differential equations; Quantum physics; Schroedinger equation; Stochastic control theory; Stochastic processes; Studies; Theory of Computation; Transport; Schrödinger bridge; 49L20; 49J20; 60J60; 35Q35; Stochastic control; Optimal transport; 28A50

We take a new look at the relation between the optimal transport problem and the Schrödinger bridge problem from a stochastic control perspective. Our aim is to highlight new connections between the two that are richer and deeper than those previously described in the literature. We begin with an el...