Deep Reinforcement Learning has been recently a very active field of research. The policies generated with use of that class of train-ing algorithms are flexible and thus have many practical applications. In this paper we present the results of our attempt to use the recent ad-vancements in Reinforcement Learning to automate the management of resources in a compute cloud environment. We describe a new approach to self-adaptation of autonomous management, which uses a digital clone of the managed infrastructure to continuously update the control policy. We present the architecture of our system and discuss the results of evaluation which includes autonomous management of a sample application deployed to Amazon Web Services cloud. We also provide the details of training of the management policy using the Proximal Policy Optimization algorithm. Finally, we discuss the feasibility to extend the presented approach to further scenarios.