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In this work, we consider the regret minimization problem for reinforcementlearning in latent Markov Decision Processes (LMDP). In an LMDP, an MDP israndomly drawn from a set of $M$ possible MDPs at the beginning of theinteraction, but the identity of the chosen MDP is not revealed to the agent.We first show that a general instance of LMDPs requires at least$\Omega((SA)^M)$ episodes to even approximate the optimal policy. Then, weconsider sufficient assumptions under which learning good policies requirespolynomial number of episodes. We show that the key link is a notion ofseparation between the MDP system dynamics. With sufficient separation, weprovide an efficient algorithm with local guarantee, {\it i.e.,} providing asublinear regret guarantee when we are given a good initialization. Finally, ifwe are given standard statistical sufficiency assumptions common in thePredictive State Representation (PSR) literature (e.g., Boots et al.) and areachability assumption, we show that the need for initialization can beremoved.

RL for Latent MDPs: Regret Guarantees and a Lower Bound