Cramér distance

The Cramér distance compares cumulative distribution functions by integrating their squared difference:

It is closely related to the energy distance, and like Wasserstein it is sensitive to how far apart probability mass is located. Unlike Wasserstein, it has unbiased sample gradients, which is useful in stochastic training.

That property motivated the Cramér GAN and its use in distributional reinforcement learning, where predicting a whole distribution of returns needs a stable loss.