Inverse Stochastic Control via Generalized Schr\"odinger Problems

TL;DR

This paper introduces a variational approach to inverse stochastic control problems, connecting them with generalized Schrödinger problems and stochastic optimal transport, providing a new perspective on inverse inference in controlled diffusions.

Contribution

It formulates inverse stochastic control as a variational problem linked to generalized Schrödinger problems, bridging inverse control with stochastic optimal transport.

Findings

Establishes a variational formulation for inverse stochastic control.

Shows the equivalence of the inverse problem with a generalized Schrödinger problem.

Provides a new conceptual framework connecting inverse control and stochastic transport.

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.