提出无需模拟的可扩展熵不平衡最优传输方法，加速生成模型训练与推理。
Scalable Simulation-free Entropic Unbalanced Optimal Transport
- 基于随机控制视角推导欧氏熵不平衡最优传输的对偶形式与最优条件
- 新算法实现训练无模拟、一步生成，相比原有方法效率显著提升
- 适用于大规模生成建模与图像翻译，特别适合追求高效推理的场景
最优传输（OT）问题研究如何在最小化给定代价函数的前提下，建立两个分布之间的传输映射。该问题在生成建模、图像到图像转换等机器学习任务中有广泛应用。本文提出一种可扩展且无需模拟的熵不平衡最优传输（EUOT）求解方法。我们推导了该问题的动力学形式，这是对Schödinger桥（SB）问题的推广。基于随机最优控制视角，我们获得了EUOT的对偶形式与最优性条件。利用这些性质，提出无需模拟的算法——仿真自由EUOT（SF-EUOT）。与现有SB模型需在训练和评估中进行高成本模拟不同，本方法实现无模拟训练与一步生成，借助互逆性质达成高效计算。实验表明，该方法在生成建模和图像到图像转换任务中相比以往SB方法展现出显著更优的可扩展性。
原文摘要 · Abstract (English)
The Optimal Transport (OT) problem investigates a transport map that connects two distributions while minimizing a given cost function. Finding such a transport map has diverse applications in machine learning, such as generative modeling and image-to-image translation. In this paper, we introduce a scalable and simulation-free approach for solving the Entropic Unbalanced Optimal Transport (EUOT) problem. We derive the dynamical form of this EUOT problem, which is a generalization of the Schrödinger bridges (SB) problem. Based on this, we derive dual formulation and optimality conditions of the EUOT problem from the stochastic optimal control interpretation. By leveraging these properties, we propose a simulation-free algorithm to solve EUOT, called Simulation-free EUOT (SF-EUOT). While existing SB models require expensive simulation costs during training and evaluation, our model achieves simulation-free training and one-step generation by utilizing the reciprocal property. Our model demonstrates significantly improved scalability in generative modeling and image-to-image translation tasks compared to previous SB methods.
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