{"ID":2828775,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12971","arxiv_id":"2512.12971","title":"A Regime-Switching Approach to the Unbalanced Schrödinger Bridge Problem","abstract":"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.","short_abstract":"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 pr...","url_abs":"https://arxiv.org/abs/2512.12971","url_pdf":"https://arxiv.org/pdf/2512.12971v1","authors":"[\"Andrei Zlotchevski\",\"Linan Chen\"]","published":"2025-12-15T04:22:57Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}