Review for NeurIPS paper: Provably Efficient Neural Estimation of Structural Equation Models: An Adversarial Approach

Summary and Contributions: The paper proposes an adversarial minimax two player game approach for optimising the parameters of a generalised structural equation model (SEM) formulated as a saddle-point problem. The generalised SEM is defined in terms of a conditional expectation operator mapping between a hilbert space of structural functions of interest to a hilbert space of known or estimated functions of the outcome. These spaces are subsequently chosen to be the space of possible neural networks and a stochastic primal-dual algorithm is given for finding a solution to the saddle-point problem. Furthermore, the work proves global convergence of the algorithm. This main result is achieved, under certain specific data and weight initialisation conditions, using a regret analysis while considering the infinite width limit for neural networks that cause them to behave like linear learners.