Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schrödinger Bridge Problem
Solutions to the Schrödinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approach is the Hopf-Cole transform that recasts the conditions for optimality into a system of boundary-coupled linear PDEs. Recent works pointed out that for the control-affine Schrödinger bridge problem, this exact linearity via Hopf-Cole transform, and thus the standard Sinkhorn recursion, apply only if the control and noise channels are proportional. When the channels do not match, the Hopf-Cole-tra...
| Authors | Georgiy A. Bondar, Asmaa Eldesoukey, Yongxin Chen et al. |
|---|---|
| Primary category | math.OC |
| Published | 25 April 2026 |
| Last updated at source | 25 April 2026 |
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