Model-Free versus Model-Driven Machine Learning

Model-free machine learning is a tabula rasa method, estimating parametric functions purely from the data. In contrast, model-driven machine learning augments mathematical models with machine learning. For example, unknown terms in SDEs and PDEs can be represented by neural networks. We compare these two approaches, discuss their mathematical theory, and present several examples. In model-free machine learning, we use reinforcement learning to train order-execution models on limit order book data. Event-by-event simulation, based on the historical order book dataset, is used to train and evaluate limit order strategies. In model-driven machine learning, we develop SDEs and PDEs with neural network terms for options pricing as well as, in an application outside of finance, predictive modeling in physics. We are able to prove global convergence of the optimization algorithm for a class of linear elliptic PDEs with neural network terms.