  Reinforcement learning algorithms are widely used in domains where it is
desirable to provide a personalized service. In these domains it is common that
user data contains sensitive information that needs to be protected from third
parties. Motivated by this, we study privacy in the context of finite-horizon
Markov Decision Processes (MDPs) by requiring information to be obfuscated on
the user side. We formulate this notion of privacy for RL by leveraging the
local differential privacy (LDP) framework. We establish a lower bound for
regret minimization in finite-horizon MDPs with LDP guarantees which shows that
guaranteeing privacy has a multiplicative effect on the regret. This result
shows that while LDP is an appealing notion of privacy, it makes the learning
problem significantly more complex. Finally, we present an optimistic algorithm
that simultaneously satisfies $\varepsilon$-LDP requirements, and achieves
$\sqrt{K}/\varepsilon$ regret in any finite-horizon MDP after $K$ episodes,
matching the lower bound dependency on the number of episodes $K$.
