The constant increase in wireless handheld devices and the prospect of billions of connected machines has led the cellular community to research many different technologies that can deliver a high data rate and quality of service to mobile users (MUs). One of the problems that is usually overlooked by the community is that more devices mean higher signaling necessary to coordinate transmission and to allocate resources effectively. In particular, channel state information (CSI) of the users' channels is necessary in order for the base station to assign frequency resources. On the other hand, this feedback (FB) information comes at a cost of uplink (UL) bandwidth, which is traditionally not considered. In this paper, we analyze the impact that reduced user FB information has on a Long-Term Evolution (LTE) network. A model, which considers the tradeoff between downlink (DL) performance and UL overhead, is presented. We introduce different FB-allocation strategies, which follow the same structure as the ones in the LTE standard, and study their effects on the network for varying number of users and different resource-allocation strategies. We show that dynamically allocating FB resources can be beneficial for the network. In order for the base station to determine which FB-allocation strategy is the most beneficial, in specific network conditions, we propose two reinforcement learning (RL) algorithms. The first solution allows the base station to allocate one homogeneous FB strategy valid for all the users served, whereas the second more complex solution determines a different strategy for each user based on its channel conditions. The RL methods show that, even in dynamic scenarios, each base station is capable of determining an optimal operating point autonomously, hence optimally balancing FB overhead and benefits.