We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a family of generator objectives that target arbitrary @math -divergences without minimizing a lower bound, and use them to train generative image models that target either improved sample quality or greater sample diversity.
Concurrent with our work, two papers propose closely related GAN training algorithms. In @cite_6 , they directly estimate the density ratio by optimizing a different discriminator objective that corresponds to rewriting the discriminator in terms of the density ratio: This approach requires learning a network that directly outputs the density ratio, which can be very small or very large and in practice the networks that parameterize the density ratio must be clipped @cite_6 . We found estimating a function of the density ratio to be more stable, in particular using the GAN discriminator objective the discriminator @math estimates @math . However, there are likely ways of combining these approaches in the future to directly estimate stable functions of the density ratio independent of the discriminator divergence.
@cite_6
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Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when learning the generator. We propose a novel algorithm that repeats the density ratio estimation and f-divergence minimization. Our algorithm offers a new perspective toward the understanding of GANs and is able to make use of multiple viewpoints obtained in the research of density ratio estimation, e.g. what divergence is stable and relative density ratio is useful.