Reinforcement Learning in System Identification

The Reinforcement Learning (RL) problem has been widely researched an applied in several areas (Sutton & Barto, 1998; Sutton, 1988; Singh & Sutton, 1996; Schapire & Warmuth, 1996; Tesauro, 1995; Si & Wang, 2001; Van Buijtenen et al., 1998). In dynamical environments, a learning agent gets rewards or penalties, according to its performance for learning good actions. In identification problems, information from the environment is needed in order to propose an approximate system model, thus, RL can be used for taking the on-line information taking. Off-line learning algorithms have reported suitable results in system identification (Ljung, 1997); however these results are bounded on the available data, their quality and quantity. In this way, the development of on-line learning algorithms for system identification is an important contribution. In this work, it is presented an on-line learning algorithm based on RL using the Temporal Difference (TD) method, for identification purposes. Here, the basic propositions of RL with TD are used and, as a consequence, the linear TD(λ) algorithm proposed in (Sutton & Barto, 1998) is modified and adapted for systems identification and the reinforcement signal is generically defined according to the temporal difference and the identification error. Thus, the main contribution of this paper is the proposition of a generic on-line identification algorithm based on RL. The proposed algorithm is applied in the parameters adjustment of a Dynamical Adaptive Fuzzy Model (DAFM) (Cerrada et al., 2002; Cerrada et al., 2005). In this case, the prediction function is a non-linear function of the fuzzy model parameters and a non-linear TD(λ) algorithm is obtained for the on-line adjustment of the DAFM parameters. In the next section the basic aspects about the RL problem and the DAFM are revised. Third section is devoted to the proposed on-line learning algorithm for identification purposes. The algorithm performance for time-varying non-linear systems identification is showed with an illustrative example in section fourth. Finally, conclusions are presented.