Recent years witnessed a remarkable increase in the availability of data and computing resources in communication networks. This contributed to the rise of data-driven over model-driven algorithms for network automation. This paper investigates a Minimization of Drive Tests (MDT)-driven Deep Reinforcement Learning (DRL) algorithm to optimize coverage and capacity by tuning antennas tilts on a cluster of cells from TIM's cellular network. We jointly utilize MDT data, electromagnetic simulations, and network Key Performance indicators (KPIs) to define a simulated network environment for the training of a Deep Q-Network (DQN) agent. Some tweaks have been introduced to the classical DQN formulation to improve the agent's sample efficiency, stability and performance. In particular, a custom exploration policy is designed to introduce soft constraints at training time. Results show that the proposed algorithm outperforms baseline approaches like DQN and best-first search in terms of long-term reward and sample efficiency. Our results indicate that MDT-driven approaches constitute a valuable tool for autonomous coverage and capacity optimization of mobile radio networks.