Because reinforcement learning suffers from a lack of scalability, online value (and Q-) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the following features: sample-efficiency, non-linear approximation, non-stationarity handling and uncertainty management. A first KTD-based algorithm is provided for deterministic Markov Decision Processes (MDP) which produces biased estimates in the case of stochastic transitions. Than the eXtended KTD framework (XKTD), solving stochastic MDP, is described. Convergence is analyzed for special cases for both deterministic and stochastic transitions. Related algorithms are experimented on classical benchmarks. They compare favorably to the state of the art while exhibiting the announced features. 1.

Abstract — A common drawback of standard reinforcement learning algorithms is their inability to scale-up to real-world problems. For this reason, a current important trend of research is (state-action) value function approximation. A prominent value function approximator is the least-squares temporal differences (LSTD) algorithm. However, for technical reasons, linearity is mandatory: the parameterization of the value function must be linear (compact nonlinear representations are not allowed) and only the Bellman evaluation operator can be considered (imposing policy-iteration-like schemes). In this paper, this restriction of LSTD is lifted thanks to a derivativefree statistical linearization approach. This way, nonlinear parameterizations and the Bellman optimality operator can be taken into account (this last point allows taking into account value-iteration-like schemes). The efficiency of the resulting algorithms are demonstrated using a linear parametrization and neural networks as well as on a Q-learning-like problem. A theoretical analysis is also provided. Index Terms — reinforcement learning, value function approximation, statistical linearization, neural networks. I.

Abstract—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. Index Terms—Reinforcement learning, value function approximation, survey. I.

Reinforcement learning is a machine learning answer to the optimal control problem. It consists in 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 subtopic of reinforcement learning is to compute an approximation of this value function when the system is too large for an exact representation. This survey reviews 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

Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists in 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 paper presents statistical-linearization-based approaches to estimate such functions. Compared to more classical approaches, this allows considering nonlinear parameterizations as well as the Bellman optimality operator, which induces some differentiability problems. Moreover, the statistical point of view adopted here allows considering colored observation noise models instead of the classical white one; in RL, this can provide useful. 1