On the Contraction Coefficient of the Schrödinger Bridge for Stochastic Linear Systems

Schrödinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schrödinger bridge problems, in both classical and in the linear system settings, is via c...

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Bibliographic Details
Published inIEEE control systems letters Vol. 7; p. 1
Main Authors Teter, Alexis M.H., Chen, Yongxin, Halder, Abhishek
Format Journal Article
LanguageEnglish
Published IEEE 01.01.2023
Subjects
Bridges
Convergence
Linear systems
Markov processes
Optimal control
Probability density function
Stochastic optimal control
stochastic systems
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ISSN2475-1456
2475-1456
DOI10.1109/LCSYS.2023.3326836

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Summary:Schrödinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schrödinger bridge problems, in both classical and in the linear system settings, is via contractive fixed point recursions. These recursions can be seen as dynamic versions of the well-known Sinkhorn iterations, and under mild assumptions, they solve the so-called Schrödinger systems with guaranteed linear convergence. In this work, we study a priori estimates for the contraction coefficients associated with the convergence of respective Schrödinger systems. We provide new geometric and control-theoretic interpretations for the same. Building on these newfound interpretations, we point out the possibility of improved computation for the worst-case contraction coefficients of linear SBPs by preconditioning the endpoint support sets.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2023.3326836