Previous results have shown that a two time-scale update rule (TTUR) using different learning rates, such as different constant rates or different decaying rates, is useful for training generative adversarial networks (GANs) in theory and in practice. Moreover, not only the learning rate but also the batch size is important for training GANs with TTURs and they both affect the number of steps needed for training. This paper studies the relationship between batch size and the number of steps needed for training GANs with TTURs based on constant learning rates. We theoretically show that, for a TTUR with constant learning rates, the number of steps needed to find stationary points of the loss functions of both the discriminator and generator decreases as the batch size increases and that there exists a critical batch size minimizing the stochastic first-order oracle (SFO) complexity. Then, we use the Fr'echet inception distance (FID) as the performance measure for training and provide numerical results indicating that the number of steps needed to achieve a low FID score decreases as the batch size increases and that the SFO complexity increases once the batch size exceeds the measured critical batch size. Moreover, we show that measured critical batch sizes are close to the sizes estimated from our theoretical results.

翻译：先前结果表明，采用不同学习率（如固定学习率或衰减学习率）的双时间尺度更新规则（TTUR）在理论和实践中对训练生成对抗网络（GANs）均有效。此外，对于采用TTUR训练的GANs，不仅学习率至关重要，批量大小同样重要，两者均影响训练所需的步数。本文研究基于固定学习率的TTUR下，批量大小与训练GANs所需步数之间的关系。我们从理论上证明，对于采用固定学习率的TTUR，随着批量增大，找到判别器和生成器损失函数驻点所需的步数均会减少，且存在一个临界批量大小，能够最小化随机一阶预言机（SFO）复杂度。接着，我们以Fréchet初始距离（FID）作为训练性能指标，提供数值结果：当批量增大时，达到低FID分数所需的步数减少；一旦批量超过测得的临界批量，SFO复杂度会增大。此外，我们表明测得的临界批量大小与理论结果估计的批量大小接近。