While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the intermediate policies. This lack of control is undesired in real-world applications where a minimum requirement is that the executed policies are guaranteed to perform at least as well as an existing baseline. In this paper, we introduce the notion of conservative exploration for average reward and finite horizon problems. We present two optimistic algorithms that guarantee (w.h.p.) that the conservative constraint is never violated during learning. We derive regret bounds showing that being conservative does not hinder the learning ability of these algorithms.