Non-linear approximations of DSGE models with neural-networks and hard-constraints

Recently a number of papers have suggested using neural-networks in order to approximate policy functions in DSGE models, while avoiding the curse of dimensionality, which for example arises when solving many HANK models, and while preserving non-linearity. One important step of this method is to represent the constraints of the economic model in question in the outputs of the neural-network. I propose, and demonstrate the advantages of, a novel approach to handling these constraints which involves directly constraining the neural-network outputs, such that the economic constraints are satisfied by construction. This is achieved by a combination of re-scaling operations that are differentiable and therefore compatible with the standard gradient descent approach used when fitting neural-networks. This has a number of attractive properties, and is shown to out-perform the penalty-based approach suggested by the existing literature, which while theoretically sound, can be poorly behaved practice for a number of reasons that I identify.