Dynamic spectrum access (DSA) is regarded as an effective and efficient technology to share radio spectrum among different networks. As a secondary user (SU), a DSA device will face two critical problems: avoiding causing harmful interference to primary users (PUs), and conducting effective interference coordination with other secondary users. These two problems become even more challenging for a distributed DSA network where there is no centralized controllers for SUs. In this paper, we investigate communication strategies of a distributive DSA network under the presence of spectrum sensing errors. To be specific, we apply the powerful machine learning tool, deep reinforcement learning (DRL), for SUs to learn "appropriate" spectrum access strategies in a distributed fashion assuming NO knowledge of the underlying system statistics. Furthermore, a special type of recurrent neural network (RNN), called the reservoir computing (RC), is utilized to realize DRL by taking advantage of the underlying temporal correlation of the DSA network. Using the introduced machine learning-based strategy, SUs could make spectrum access decisions distributedly relying only on their own current and past spectrum sensing outcomes. Through extensive experiments, our results suggest that the RC-based spectrum access strategy can help the SU to significantly reduce the chances of collision with PUs and other SUs. We also show that our scheme outperforms the myopic method which assumes the knowledge of system statistics, and converges faster than the Q-learning method when the number of channels is large.