Vol: 54(68) No: 4 / December 2009 

Extending Fuzzy Q-learning with Fuzzy Rule Interpolation Method “FIVE”
Dávid Vincze
Department of Information Technology, University of Miskolc, Faculty of Mechanical Engineering and Information Science, 3515 Miskolc, Hungary, phone: (+36) 46-565-333, e-mail: david.vincze@iit.uni-miskolc.hu, web: www.iit.uni-miskolc.hu/~vinczed
Szilveszter Kovács
Department of Information Technology, University of Miskolc, Faculty of Mechanical Engineering and Information Science, 3515 Miskolc, Hungary, e-mail: szkovacs@iit.uni-miskolc.hu, web: www.iit.uni-miskolc.hu/~szkovacs


Keywords: reinforcement learning, fuzzy Q-learning, fuzzy rule interpolation.

Abstract
Fuzzy Q-learning, the fuzzy extension of the Reinforcement Learning (RL) is a well known topic in computational intelligence. It can be used to solve control problems in continuous unknown environments without defining an exact method on how to solve problems in various situations. In the RL concept the problem to be solved is hidden in the feedback of the environment, called reward or punishment (positive or negative reward). From these rewards the system can learn which action is considered to be the best choice in a given state. One of the most frequently applied RL method is the “Q-learning”. The goal of the Q-learning method is to find an optimal policy for the system by building the state-action-value function. The state-action-value-function is a function of the expected return (a function of the cumulative reinforcements), related to a given state and a taken action following the optimal policy. The original Q-learning method was introduced for discrete states and actions. With the application of fuzzy reasoning the method can be adapted for continuous environment, called Fuzzy Q-learning (FQ-Learning). Traditional Fuzzy Q-learning embeds the 0-order Takagi-Sugeno fuzzy inference and hence the requirement of the state-action-value-function representation as a complete fuzzy rule base. The main goal of this paper is to introduce an extension of the traditional fuzzy Q-learning method with the capability of handling sparse fuzzy rule-bases. To achieve this, the paper suggests to apply Fuzzy Rule Interpolation (FRI), namely the FIVE (Fuzzy rule Interpolation based on Vague Environment) to be the model applied with Q-learning (FRIQ-learning). The paper also includes an application example, the well known cart pole (reversed pendulum) problem, for demonstrating the applicability of the suggested FRIQ-learning.

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