Reviews: Minimax Estimation of Neural Net Distance

This paper considers the minimax estimation problem of neural net distance. The problem originates from the generative adversarial networks (GANs). In particular, the paper established the lower bound on the minimax estimation for neural net distance which seems to the first result of this kind. The authors then derived an upper bound on the estimation error which matches the minimax lower bound in terms of the order of sample size, and the norm of the parameter matrices. However, there is a gap of \sqrt{d} or \sqrt{d h} which remains as an open question.