← 研踪 PaperTrailarXiv:2611.11649 · v1
A Trust Region Approach for Learning Schrödinger Bridges
首次提交 2026-11-09 06:13
版本更新 2026-11-09 06:13
雷达观测 2026-11-10 13:19
摘要
We study the numerical approximation of Schrödinger Bridges in the setting where samples from the target distribution are unavailable and only an unnormalized target density is given. In this regime, the widely used iterative proportional fitting (IPF) procedure (and its variants) often exhibits severe numerical instabilities, stemming from ill-conditioned underlying control problems and from the fact that the optimal solution may lie far from the initialization. To address these issues, we propose a trust region variant of IPF that constrains successive updates to remain at a fixed Kullback-Leibler divergence from the current iterate. This restriction significantly improves numerical stability. Moreover, we show that the resulting method admits an interpretation as a mirror descent scheme with an adaptively chosen step size. We demonstrate the effectiveness of our approach on several challenging sampling tasks.
作者备注：Accepted to NeurIPS 2026; Takeshi Koshizuka and Lorenz Richter contributed equally
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v1 · 2026-11-09 06:13 · 最新观测版本
A Trust Region Approach for Learning Schrödinger Bridges
We study the numerical approximation of Schrödinger Bridges in the setting where samples from the target distribution are unavailable and only an unnormalized target density is given. In this regime, the widely used iterative proportional fitting (IPF) procedure (and its variants) often exhibits severe numerical instabilities, stemming from ill-conditioned underlying control problems and from the fact that the optimal solution may lie far from the initialization. To address these issues, we propose a trust region variant of IPF that constrains successive updates to remain at a fixed Kullback-Leibler divergence from the current iterate. This restriction significantly improves numerical stability. Moreover, we show that the resulting method admits an interpretation as a mirror descent scheme with an adaptively chosen step size. We demonstrate the effectiveness of our approach on several challenging sampling tasks.
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