Optimal service and resource management in Fog Computing is an active research area in academia. In fact, to fulfill the promise to enable a new generation of immersive, adaptive, and context-aware services, Fog Computing requires novel solutions capable of better exploiting the available computational and network resources at the edge. Resource management in Fog Computing could particularly benefit from self-* approaches capable of learning the best resource allocation strategies to adapt to the ever changing conditions. In this context, Reinforcement Learning (RL), a technique that allows to train software agents to learn which actions maximize a reward, represents a compelling solution to investigate. In this paper, we explore RL as an optimization method for the value-based management of Fog services over a pool of Fog nodes. More specifically, we propose FogReinForce, a solution based on Deep Q-Network (DQN) algorithm that learns to select the allocation for service components that maximizes the value-based utility provided by those services.