Cognitive radio technologies have been developed to utilize the limited spectrum resources and optimize the behavior of the radio system, along with the variable radio status, by intelligent learning. The optimization can be achieved through clarifying the relationship among certain variables and target performance indices. However, today's wireless systems are becoming increasingly complex due to the advances of wireless technologies; this increases the number of variables of the optimization problem, which makes the relations among the variables and system performance to be formulated with difficulty. Recent advance in the field of machine learning technologies can help us overcome such difficulties by adopting for cognitive radio systems. This paper proposes a cross-layer modeling of wireless system using machine learning and optimization method based on cognitive cycle. The experimental evaluation is shown by applying the method to the IEEE 802.11 wireless local area network.