Interpretable policies for reinforcement learning by empirical fuzzy sets

This paper proposes a method and an algorithm to implement interpretable fuzzy reinforcement learning (IFRL). It provides alternative solutions to common problems in RL, like function approximation and continuous action space. The learning process resembles that of human beings by clustering the encountered states, developing experiences for each of the typical cases, and making decisions fuzzily. The learned policy can be expressed as human-intelligible IF-THEN rules, which facilitates further investigation and improvement. It adopts the actor–critic architecture whereas being different from mainstream policy gradient methods. The value function is approximated through the fuzzy system AnYa. The state–action space is discretized into a static grid with nodes. Each node is treated as one prototype and corresponds to one fuzzy rule, with the value of the node being the consequent. Values of consequents are updated using the Sarsa() algorithm. Probability distribution of optimal actions regarding different states is estimated through Empirical Data Analytics (EDA), Autonomous Learning Multi-Model Systems (ALMMo), and Empirical Fuzzy Sets ( ε FS). The fuzzy kernel of IFRL avoids the lack of interpretability in other methods based on neural networks. Simulation results with four problems, namely Mountain Car, Continuous Gridworld, Pendulum Position, and Tank Level Control, are presented as a proof of the proposed concept

Stability of Evolving Fuzzy Systems Based on Data Clouds

Evolving fuzzy systems (EFSs) are now well developed and widely used, thanks to their ability to self-adapt both their structures and parameters online. Since the concept was first introduced two decades ago, many different types of EFSs have been successfully implemented. However, there are only very few works considering the stability of the EFSs, and these studies were limited to certain types of membership functions with specifically predefined parameters, which largely increases the complexity of the learning process. At the same time, stability analysis is of paramount importance for control applications and provides the theoretical guarantees for the convergence of the learning algorithms. In this paper, we introduce the stability proof of a class of EFSs based on data clouds, which are grounded at the AnYa type fuzzy systems and the recently introduced empirical data analytics (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this paper avoids the traditional way of defining membership functions for each input variable in an explicit manner and its learning process is entirely data driven. The stability of the considered EFS of AnYa type is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. Although, the stability proof presented in this paper is specially elaborated for the considered EFS, it is also applicable to general EFSs. The proposed method is illustrated with Box-Jenkins gas furnace problem, one nonlinear system identification problem, Mackey-Glass time series prediction problem, eight real-world benchmark regression problems as well as a high-frequency trading prediction problem. Compared with other EFSs, the numerical examples show that the considered EFS in this paper provides guaranteed stability as well as a better approximation accuracy