  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.
