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

Abstract

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space S and the action space A are both finite, to obtain a nearly optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with |S||A|, which can be prohibitively large when S or A 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 K(1-)^3^2 (resp.~K(1-)^4^2), up to some logarithmic factor. Here K 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 K is relatively small, and hence the title of this paper.

Tasks

Reproductions