While the field of continuous Entropic Optimal Transport (EOT) has been actively developing in recent years, it became evident that the classic EOT problem is prone to different issues like the sensitivity to outliers and imbalance of classes in the source and target measures. This fact inspired the development of solvers which deal with the unbalanced EOT (UEOT) problem - the generalization of EOT allowing for mitigating the mentioned issues by relaxing the marginal constraints. Surprisingly, it turns out that the existing solvers are either based on heuristic principles or heavy-weighted with complex optimization objectives involving several neural networks. We address this challenge and propose a novel theoretically-justified and lightweight unbalanced EOT solver. Our advancement consists in developing a novel view on the optimization of the UEOT problem yielding tractable and non-minimax optimization objective. We show that combined with a light parametrization recently proposed in the field our objective leads to fast, simple and effective solver. It allows solving the continuous UEOT problem in minutes on CPU. We provide illustrative examples of the performance of our solver.

翻译：尽管连续熵最优传输（EOT）领域近年来发展活跃，但经典EOT问题逐渐暴露出对异常值敏感、源测度与目标测度中类别不平衡等缺陷。这一事实推动了处理不平衡EOT（UEOT）问题的求解器研发——作为EOT的推广形式，UEOT通过放宽边际约束有效缓解了上述问题。令人意外的是，现有求解器要么依赖启发式原则，要么因涉及多个神经网络的复杂优化目标而过于繁重。我们针对这一挑战，提出了理论上严谨且轻量的不平衡EOT求解器。我们的突破在于构建了UEOT问题优化的全新视角，从而得到可解的非极小化优化目标。研究表明，结合该领域近期提出的轻量参数化方法，该目标能实现快速、简洁且高效的求解。该求解器可在CPU上数分钟内求解连续UEOT问题。我们通过实例展示了该求解器的性能表现。