用深度粒子方法计算分布间最优传输映射，有收敛保证。
DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee
- 基于深度粒子方法构建可训练的最优传输映射
- 理论证明学习映射与真实映射误差有量化上界
- 无需网络结构限制，适合真实数据任务
本文提出一种新的机器学习方法，通过深度粒子方法从无配对样本中计算两个连续分布间的最优传输映射。该方法在训练过程中形成双极小优化问题，不依赖特定网络结构。理论上建立了弱收敛性保证及学习映射与最优传输映射之间的定量误差上界。数值实验验证了理论结果的有效性，尤其在真实世界任务中表现优异。
原文摘要 · Abstract (English)
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments validate the theoretical results and the effectiveness of the new approach, particularly on real-world tasks.
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