OTGANs

OTGANs, or Optimal Transport GANs, are a class of generative models that incorporate optimal transport theory into the framework of generative adversarial networks. The central idea is to measure the discrepancy between the real data distribution and the model’s generated distribution using an optimal transport distance, rather than traditional divergences like Jensen-Shannon. This distance reflects the minimum cost of morphing one distribution into the other under a specified transport cost.

In OTGAN formulations, the transport distance between real samples x and generated samples G(z) is defined with a cost function c(x, y). Through Kantorovich duality, this distance can be expressed in a form that resembles a critic function, often referred to as a potential. A neural network serves as this critic, estimating the transport potential and guiding the generator to produce samples that reduce the transport cost. Training typically alternates between updating the critic to better approximate the optimal transport plan and updating the generator to minimize the estimated transport cost.

Computationally, OTGANs frequently employ regularization strategies to make the transport problem tractable. Entropic regularization leads to Sinkhorn-type approximations, while alternatives like sliced optimal transport reduce complexity by projecting data onto lower-dimensional directions. The cost function can itself be parameterized by neural networks to capture complex transport costs between data modalities.

OTGANs are related to, and in some respects complement, Wasserstein GANs and other OT-based methods. They aim to improve training stability and sample quality, with particular emphasis on better mode coverage and robustness to optimization difficulties, albeit at increased computational cost and with sensitivity to the chosen transport cost and regularization.