Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial markets

We develop a new topological structure for the construction of a reinforcement learning model in the framework of financial markets. It is based on Lipschitz type extension of reward functions defined in metric spaces. Using some known states of a dynamical system that represents the evolution of a financial market, we use our technique to simulate new states, that we call ``dreams". These new states are used to feed a learning algorithm designed to improve the investment strategy.