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arXiv · 2601.09210

Inverse Stochastic Control via Generalized Schr\"odinger Problems

Yumiharu Nakano
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Abstract

We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the suboptimality gap of observed behavior. We establish a connection between the inverse problem and a generalized dynamic Schr\"odinger problem, showing that their optimal values coincide. This result links inverse stochastic control with stochastic optimal transport, offering a new conceptual viewpoint on inverse inference in controlled diffusions.

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Yumiharu Nakano. 2026-01-14. Inverse Stochastic Control via Generalized Schr\"odinger Problems. https://arxiv.org/abs/2601.09210

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