We view variational autoencoders (VAE) as decoder-encoder pairs, which map distributions in the data space to distributions in the latent space and vice versa. The standard learning approach for VAEs, i.e. maximisation of the evidence lower bound (ELBO), has an obvious asymmetry in that respect. Moreover, it requires a closed form a-priori latent distribution. This limits the applicability of VAEs in more complex scenarios, such as general semi-supervised learning and employing complex generative models as priors. We propose a Nash equilibrium learning approach that relaxes these restrictions and allows learning VAEs in situations where both the data and the latent distributions are accessible only by sampling. The flexibility and simplicity of this approach allows its application to a wide range of learning scenarios and downstream tasks. We show experimentally that the models learned by this method are comparable to those obtained by ELBO learning and demonstrate its applicability for tasks that are not accessible by standard VAE learning.

翻译：我们将变分自编码器（VAE）视为解码器-编码器对，它们将数据空间中的分布映射到隐空间中的分布，反之亦然。标准VAE学习方法（即最大化证据下界）在这方面存在明显的不对称性。此外，它需要闭式先验隐分布。这限制了VAE在更复杂场景（如通用半监督学习和使用复杂生成模型作为先验）中的适用性。我们提出一种纳什平衡学习方法，该方法放宽了这些限制，并允许在数据和隐分布仅能通过采样获取的情况下学习VAE。该方法的灵活性和简洁性使其适用于广泛的学习场景和下游任务。实验表明，通过该方法学习的模型与通过ELBO学习获得的模型性能相当，并展示了其在标准VAE学习无法适用的任务中的实用性。