Despite the recent advances in the field of computational Schrodinger Bridges
(SB), most existing SB solvers are still heavy-weighted and require complex
optimization of several neural networks. It turns out that there is no
principal solver which plays the role of simple-yet-effective baseline for SB
just like, e.g., $k$-means method in clustering, logistic regression in
classification or Sinkhorn algorithm in discrete optimal transport. We address
this issue and propose a novel fast and simple SB solver. Our development is a
smart combination of two ideas which recently appeared in the field: (a)
parameterization of the Schrodinger potentials with sum-exp quadratic functions
and (b) viewing the log-Schrodinger potentials as the energy functions. We show
that combined together these ideas yield a lightweight, simulation-free and
theoretically justified SB solver with a simple straightforward optimization
objective. As a result, it allows solving SB in moderate dimensions in a matter
of minutes on CPU without a painful hyperparameter selection. Our light solver
resembles the Gaussian mixture model which is widely used for density
estimation. Inspired by this similarity, we also prove an important theoretical
result showing that our light solver is a universal approximator of SBs. The
code for the LightSB solver can be found at
this https URL

在计算薛定谔桥（SB）领域中，通过参数化薛定谔势能和将对数薛定谔势能视为能量函数的智能组合，我们提出了一种新颖的快速简洁的 SB 求解器，该求解器是一个轻量级、无需模拟且理论验证的求解器，适用于中等维度的 SB 问题。