GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
Martin Heusel、Hubert Ramsauer、Thomas Unterthiner、Bernhard Nessler、Sepp Hochreiter LIT AI Lab、Institute of Bioinformatics, Johannes Kepler University Linz A-4040 Linz, Austria
Abstract
Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the ‘Fréchet Inception Distance” (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.
中文速览
生成对抗网络（GAN）在训练时极易出现不收敛和模式崩溃（mode collapse）的问题，根本原因在于判别器和生成器同步更新时会相互干扰、陷入震荡。这篇论文提出了"双时间尺度更新规则"（Two Time-Scale Update Rule，TTUR）：给判别器和生成器分别设置不同的学习率，让判别器"跑得快"、生成器"跑得慢"，借助随机逼近理论严格证明了这种设置能收敛到局部纳什均衡；同时证明了常用的 Adam 优化器本质上等价于带摩擦的重球（Heavy Ball with Friction）动力学，天然倾向于落入平坦的极小值区域，从而与 TTUR 配合使用时也能保证收敛并抑制模式崩溃。此外，论文还提出了"弗雷歇初始距离"（Fréchet Inception Distance，FID）这一新的图像生成质量评估指标，在统计上比此前流行的 Inception Score 更能反映生成图像与真实图像分布的相似程度。实验表明，TTUR 在 CelebA、CIFAR-10 等多个基准上显著优于标准 GAN 训练，FID 也成为此后领域内广泛采用的标准评估工具。
原文 arXiv:1706.08500;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1706.08500v6