Parametric value function approximation: A unified view

Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists of learning an optimal control policy through interactions with the system to be controlled, the quality of this policy being quantified by the so-called value function. An important RL subtopic is to approximate this function when the system is too large for an exact representation. This survey reviews and unifies state of the art methods for parametric value function approximation by grouping them into three main categories: bootstrapping, residuals and projected fixed-point approaches. Related algorithms are derived by considering one of the associated cost functions and a specific way to minimize it, almost always a stochastic gradient descent or a recursive least-squares approach.