Generative adversarial networks (GANs) have emerged as a powerful tool for generating high-fidelity data. However, the main bottleneck of existing approaches is the lack of supervision on the generator training, which often results in undamped oscillation and unsatisfactory performance. To address this issue, we propose an algorithm called Monte Carlo GAN (MCGAN). This approach, utilizing an innovative generative loss function, termly the regression loss, reformulates the generator training as a regression task and enables the generator training by minimizing the mean squared error between the discriminator's output of real data and the expected discriminator of fake data. We demonstrate the desirable analytic properties of the regression loss, including discriminability and optimality, and show that our method requires a weaker condition on the discriminator for effective generator training. These properties justify the strength of this approach to improve the training stability while retaining the optimality of GAN by leveraging strong supervision of the regression loss. Numerical results on CIFAR-10 and CIFAR-100 datasets demonstrate that the proposed MCGAN significantly and consistently improves the existing state-of-the-art GAN models in terms of quality, accuracy, training stability, and learned latent space. Furthermore, the proposed algorithm exhibits great flexibility for integrating with a variety of backbone models to generate spatial images, temporal time-series, and spatio-temporal video data.

翻译：生成对抗网络（GAN）已成为生成高保真数据的强大工具。然而，现有方法的主要瓶颈在于生成器训练缺乏监督，这通常导致无阻尼振荡和性能不佳。为解决此问题，我们提出一种称为蒙特卡洛GAN（MCGAN）的算法。该方法利用创新的生成器损失函数（称为回归损失），将生成器训练重构为回归任务，并通过最小化真实数据判别器输出与生成数据期望判别器之间的均方误差来实现生成器训练。我们证明了回归损失具备理想的解析性质，包括可判别性和最优性，并表明我们的方法在有效生成器训练中对判别器的条件要求更弱。这些性质证明了该方法在保持GAN最优性的同时，通过利用回归损失的强监督来提高训练稳定性的优势。在CIFAR-10和CIFAR-100数据集上的数值结果表明，所提出的MCGAN在生成质量、精度、训练稳定性和学习到的潜在空间方面显著且持续地改进了现有最先进的GAN模型。此外，所提算法展现出与多种骨干模型结合的强大灵活性，可用于生成空间图像、时序时间序列和时空视频数据。