  A method of a fusion of fuzzy inference and policy gradient reinforcement
learning has been proposed that directly learns, as maximizes the expected
value of the reward per episode, parameters in a policy function represented by
fuzzy rules with weights. A study has applied this method to a task of speed
control of an automobile and has obtained correct policies, some of which
control speed of the automobile appropriately but many others generate
inappropriate vibration of speed. In general, the policy is not desirable that
causes sudden time change or vibration in the output value, and there would be
many cases where the policy giving smooth time change in the output value is
desirable. In this paper, we propose a fusion method using the objective
function, that introduces defuzzification with the center of gravity model
weighted stochastically and a constraint term for smoothness of time change, as
an improvement measure in order to suppress sudden change of the output value
of the fuzzy controller. Then we show the learning rule in the fusion, and also
consider the effect by reward functions on the fluctuation of the output value.
As experimental results of an application of our method on speed control of an
automobile, it was confirmed that the proposed method has the effect of
suppressing the undesirable fluctuation in time-series of the output value.
Moreover, it was also showed that the difference between reward functions might
adversely affect the results of learning.
