Schr”odinger bridge problem via empirical risk minimization
arXiv:2602.08374v1 Announce Type: new Abstract: We study the Schr”odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr”odinger potentials via Sinkhorn iterations on empirical measures and then construct a time-inhomogeneous drift by differentiating a kernel-smoothed dual solution. In contrast, we propose a learning-theoretic route: we rewrite the Schr”odinger system in terms of a single positive transformed potential that satisfies a nonlinear fixed-point equation and estimate this potential by empirical risk minimization […]