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 https://github.com/ngushchin/LightSB

翻译：尽管计算薛定谔桥（SB）领域近期取得了进展，但现有的大多数SB求解器仍然过于复杂，需要对多个神经网络进行复杂的优化。目前尚缺乏一个类似于聚类中的$k$-均值方法、分类中的逻辑回归或离散最优输运中的Sinkhorn算法那样，既简单又有效的SB基准求解器。针对这一问题，我们提出了一种新颖、快速且简单的SB求解器。我们的方法巧妙结合了该领域近期出现的两个思路：（a）利用和二次指数函数参数化薛定谔势；（b）将对数薛定谔势视为能量函数。我们证明，将这两个思路结合，可以得到一个轻量级、免模拟且具有理论依据的SB求解器，其优化目标简单直接。因此，该求解器能在CPU上仅用数分钟解决中等维度的SB问题，且无需繁琐的超参数选择。我们的轻量求解器类似于广泛用于密度估计的高斯混合模型。受此相似性启发，我们还证明了一个重要的理论结果：我们的轻量求解器是SB的通用近似器。LightSB求解器的代码可在https://github.com/ngushchin/LightSB获取。