Explaining what a reinforcement learning (RL) control agent learns play a crucial role in the safety critical control domain. Most of the approaches in the state-of-the-art focused on imitation learning methods that uncover the hidden reward function of a given control policy. However, these approaches do not uncover what the RL agent learns effectively from the agent-environment interaction. The policy learned by the RL agent depends in how good the state transition mapping is inferred from the data. When the state transition mapping is wrongly inferred implies that the RL agent is not learning properly. This can compromise the safety of the surrounding environment and the agent itself. In this paper, we aim to uncover the elements learned by data-driven RL control agents in a special class of discrete-time linear autonomous systems. Here, the approach aims to add a new explainable dimension to data-driven control approaches to increase their trust and safe deployment. We focus on the classical data-driven Q-learning algorithm and propose an explainable Q-learning (XQL) algorithm that can be further expanded to other data-driven RL control agents. Simulation experiments are conducted to observe the effectiveness of the proposed approach under different scenarios using several discrete-time models of autonomous platforms.

Uncovering the reward function of optimal controllers is crucial to determine the desired performance that an expert wants to inject to a certain dynamical system. In this paper, a reward inference algorithm of discrete-time expert's controllers is proposed. The approach is inspired by the complementary mechanisms of the striatum, neocortex, and hippocampus for decision making and experience transference. These systems work together to infer the reward function associated to expert's controller using the complementary merits of data-driven and online learning methods. The proposed approach models the neocortex system as two independent learning algorithms given by a Q-learning algorithm and a gradient identification rule. The hippocampus is modelled by a least-squares update rule that extracts the relation from the states and control inputs of the expert's data. The striatum is modelled by an inverse optimal control algorithm which iteratively finds the hidden reward function. Lyapunov stability theory is used to show the stability and convergence of the proposed approach. Simulation studies are given to demonstrate the effectiveness of the proposed complementary learning algorithm.

In this paper, a Q-learning algorithm is proposed to solve the linear quadratic regulator problem of black box linear systems. The algorithm only has access to input and output measurements. A Luenberger observer parametrization is constructed using the control input and a new output obtained from a factorization of the utility function. An integral reinforcement learning approach is used to develop the Q-learning approximator structure. A gradient descent update rule is used to estimate on-line the parameters of the Q-function. Stability and convergence of the Q-learning algorithm under the Luenberger observer parametrization is assessed using Lyapunov stability theory. Simulation studies are carried out to verify the proposed approach.