Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model.

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space and the action space are both finite, to obtain a nearly optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with , which can be prohibitively large when or is large. This paper considers a Markov decision process (MDP) that admits a set of state-action features, which can linearly express (or approximate) its probability transition kernel. We show that a model-based approach (resp. Q-learning) provably learns an -optimal policy (resp. Q-function) with high probability as soon as the sample size exceeds the order of , up to some logarithmic factor. Here is the feature dimension and ∈ (0, 1) is the discount factor of the MDP. Both sample complexity bounds are provably tight, and our result for the model-based approach matches the minimax lower bound. Our results show that for arbitrarily large-scale MDP, both the model-based approach and Q-learning are sample-efficient when is relatively small, and hence the title of this paper.