This paper develops a simulation-based solution method to solve large state space macrofinance models using machine learning. We use a neural network (NN) to approximate the expectations in the optimality conditions in the spirit of the stochastic parameterized expectations algorithm (PEA). Because our method can process the entire information set at once, it is scalable and can handle models with large and multicollinear state spaces. We demonstrate the computational gains by extending the optimal government debt management problem studied by Faraglia et al. (2019) from two to three maturities. We find that the optimal policy prescribes an active role for the newly added medium-term maturity, enabling the planner to raise financial income without increasing its total borrowing in response to expenditure shocks. Through this mechanism the government effectively subsidizes the private sector in recessions, resulting in a welfare gain of 2.38% when the number of available maturities increases from two to three.