  In many reinforcement learning (RL) problems, it takes some time until a
taken action by the agent reaches its maximum effect on the environment and
consequently the agent receives the reward corresponding to that action by a
delay called action-effect delay. Such delays reduce the performance of the
learning algorithm and increase the computational costs, as the reinforcement
learning agent values the immediate rewards more than the future reward that is
more related to the taken action. This paper addresses this issue by
introducing an applicable enhanced Q-learning method in which at the beginning
of the learning phase, the agent takes a single action and builds a function
that reflects the environments response to that action, called the reflexive
$\gamma$ - function. During the training phase, the agent utilizes the created
reflexive $\gamma$- function to update the Q-values. We have applied the
developed method to a structural control problem in which the goal of the agent
is to reduce the vibrations of a building subjected to earthquake excitations
with a specified delay. Seismic control problems are considered as a complex
task in structural engineering because of the stochastic and unpredictable
nature of earthquakes and the complex behavior of the structure. Three
scenarios are presented to study the effects of zero, medium, and long
action-effect delays and the performance of the Enhanced method is compared to
the standard Q-learning method. Both RL methods use neural network to learn to
estimate the state-action value function that is used to control the structure.
The results show that the enhanced method significantly outperforms the
performance of the original method in all cases, and also improves the
stability of the algorithm in dealing with action-effect delays.
