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Reflected Schr"odinger Bridge: Density Control with Path Constraints

arXiv 2003.13895 ↗First posted 31 Mar 2020math.OC cs.LG cs.SYcited by 22

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Abstract (arXiv)

How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety requirements such as obstacle avoidance. In this paper, we perform the feedback synthesis for minimum control effort density steering (a.k.a. Schr"odinger bridge) problem subject to state constraints. We extend the theory of Schr"odinger bridges to account the reflecting boundary conditions for the sample paths, and provide a computational framework building on our previous work on proximal recursions, to solve the same.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Mar 2020.

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Citing papers per year: 2022: 3; 2023: 5; 2024: 6; 2025: 1; 2026: 7.

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  1. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  2. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  3. 2024Schr"odinger Bridge with Quadratic State Cost is Exactly Solvablecited by 12
  4. 2023Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assemblycited by 10
  5. 2022A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assemblycited by 9
  6. 2023Transport with Support: Data-Conditional Diffusion Bridgescited by 9
  7. 2025On the Hopf-Cole Transform for Control-affine Schr"odinger Bridgecited by 5
  8. 2023On the Contraction Coefficient of the Schr"odinger Bridge for Stochastic Linear Systemscited by 3
  9. 2024Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schr"odinger Bridge and Reaction-Diffusion PDEscited by 3
  10. 2024Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridgecited by 3
  11. 2024Weyl Calculus and Exactly Solvable Schr"odinger Bridges with Quadratic State Costcited by 3
  12. 2026A Generalized Sinkhorn Algorithm for Mean-Field Schr"odinger Bridgecited by 3
10 more
  1. 2026Schr"odinger Bridge Over A Compact Connected Lie Groupcited by 2
  2. 2026Mean-Field Path-Integral Diffusion: From Samples to Interacting Agentscited by 2
  3. 2022Proximal Mean Field Learning in Shallow Neural Networkscited by 1
  4. 2023Optimal Mass Transport over the Euler Equationcited by 1
  5. 2026Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schr"odinger Bridge Problemcited by 1
  6. 2026Nonlocal Mean Field Schr"odinger Bridge with Learned Interactionscited by 1
  7. 2022A Distributed Algorithm for Measure-valued Optimization with Additive Objectivecited by 0
  8. 2024Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Modelscited by 0
  9. 2026Reflected Schr"odinger Bridge Matchingcited by 0
  10. 2026On the Equivalence of Stochastic Control and Path Space Formulations for Schr"odinger Bridges over Compact Connected Lie Groupscited by 0