Reward-Mixing MDPs with a Few Latent Contexts are Learnable
This addresses episodic reinforcement learning for scenarios with hidden reward models, offering theoretical guarantees for sample efficiency, though it is incremental as it extends prior work from M=2 to arbitrary M.
The paper tackles the problem of learning near-optimal policies in reward-mixing Markov decision processes (RMMDPs) with multiple latent reward contexts, providing a sample-efficient algorithm that outputs an ε-optimal policy using a specified number of episodes and establishing a lower bound showing super-polynomial sample complexity in M is necessary.
We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP throughout the episode for $H$ time steps. Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model. Previous work established an upper bound for RMMDPs for $M=2$. In this work, we resolve several open questions remained for the RMMDP model. For an arbitrary $M\ge2$, we provide a sample-efficient algorithm--$\texttt{EM}^2$--that outputs an $ε$-optimal policy using $\tilde{O} \left(ε^{-2} \cdot S^d A^d \cdot \texttt{poly}(H, Z)^d \right)$ episodes, where $S, A$ are the number of states and actions respectively, $H$ is the time-horizon, $Z$ is the support size of reward distributions and $d=\min(2M-1,H)$. Our technique is a higher-order extension of the method-of-moments based approach, nevertheless, the design and analysis of the \algname algorithm requires several new ideas beyond existing techniques. We also provide a lower bound of $(SA)^{Ω(\sqrt{M})} / ε^{2}$ for a general instance of RMMDP, supporting that super-polynomial sample complexity in $M$ is necessary.