A Mean-Field Analysis of Neural Gradient Descent-Ascent: Applications to Functional Conditional Moment Equations

arXiv:2404.12312v1 Announce Type: new
Abstract: We study minimax optimization problems defined over infinite-dimensional function classes. In particular, we restrict the functions to the class of overparameterized two-layer neural networks and study (i) the convergence of the gradient descent-ascent algorithm and (ii) the representation learning of the neural network. As an initial step, we consider the minimax optimization problem stemming from estimating a functional equation defined by conditional expectations via adversarial estimation, where the objective function is quadratic in the functional …

abstract algorithm analysis applications arxiv class convergence cs.lg function functional functions gradient layer math.oc mean minimax moment networks neural networks optimization representation representation learning stat.ml study type