In this paper, we focus on analyzing the excess risk of the unpaired data generation model, called CycleGAN. Unlike classical GANs, CycleGAN not only transforms data between two unpaired distributions but also ensures the mappings are consistent, which is encouraged by the cycle-consistency term unique to CycleGAN. The increasing complexity of model structure and the addition of the cycle-consistency term in CycleGAN present new challenges for error analysis. By considering the impact of both the model architecture and training procedure, the risk is decomposed into two terms: approximation error and estimation error. These two error terms are analyzed separately and ultimately combined by considering the trade-off between them. Each component is rigorously analyzed; the approximation error through constructing approximations of the optimal transport maps, and the estimation error through establishing an upper bound using Rademacher complexity. Our analysis not only isolates these errors but also explores the trade-offs between them, which provides a theoretical insights of how CycleGAN's architecture and training procedures influence its performance.

翻译：本文重点分析非配对数据生成模型CycleGAN的泛化误差。与传统GAN不同，CycleGAN不仅实现两个非配对分布间的数据转换，还通过其特有的循环一致性约束确保映射的一致性。CycleGAN模型结构的日益复杂及循环一致性项的引入，为误差分析带来了新的挑战。通过综合考虑模型架构与训练过程的影响，我们将风险分解为两个部分：近似误差与估计误差。这两类误差项分别进行分析，最终通过权衡二者关系进行整合。每个分量均经过严格分析：通过构建最优传输映射的近似函数来研究近似误差，利用Rademacher复杂度建立上界来研究估计误差。我们的分析不仅分离了这些误差，还深入探讨了其间的权衡关系，从而为理解CycleGAN架构与训练过程如何影响其性能提供了理论依据。