A Regime-Switching Approach to the Unbalanced Schrödinger Bridge Problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909962877272064 |
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| author | Zlotchevski, Andrei Chen, Linan |
| author_facet | Zlotchevski, Andrei Chen, Linan |
| contents | The unbalanced Schrödinger bridge problem (uSBP) seeks to interpolate between a probability measure $ρ_0$ and a sub-probability measure $ρ_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In this work, we investigate the case where $\mathbf{R}$ is the path measure of a diffusion process with killing, which we interpret as a regime-switching diffusion. In addition to matching the initial and terminal distributions of trajectories that survive up to time $T$, we consider a general constraint $ψ(t,x)$ on the distribution of killing times and/or killing locations.
We investigate the uSBPs corresponding to four choices of $ψ$ in detail which reflect different levels of information available to an observer. We also provide a rigorous analysis of the connections and the comparisons among the outcomes of these four cases. Our results are novel in the field of uSBP. The regime-switching approach proposed in this work provides a unified framework for tackling different uSBP scenarios, which not only reconciles but also extends the existing literature on uSBP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Regime-Switching Approach to the Unbalanced Schrödinger Bridge Problem Zlotchevski, Andrei Chen, Linan Probability Optimization and Control 35Q93, 60H10, 60H30, 60J60, 93E20, 94A17 The unbalanced Schrödinger bridge problem (uSBP) seeks to interpolate between a probability measure $ρ_0$ and a sub-probability measure $ρ_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In this work, we investigate the case where $\mathbf{R}$ is the path measure of a diffusion process with killing, which we interpret as a regime-switching diffusion. In addition to matching the initial and terminal distributions of trajectories that survive up to time $T$, we consider a general constraint $ψ(t,x)$ on the distribution of killing times and/or killing locations. We investigate the uSBPs corresponding to four choices of $ψ$ in detail which reflect different levels of information available to an observer. We also provide a rigorous analysis of the connections and the comparisons among the outcomes of these four cases. Our results are novel in the field of uSBP. The regime-switching approach proposed in this work provides a unified framework for tackling different uSBP scenarios, which not only reconciles but also extends the existing literature on uSBP. |
| title | A Regime-Switching Approach to the Unbalanced Schrödinger Bridge Problem |
| topic | Probability Optimization and Control 35Q93, 60H10, 60H30, 60J60, 93E20, 94A17 |
| url | https://arxiv.org/abs/2512.12971 |