  Incorporating expert demonstrations has empirically helped to improve the
sample efficiency of reinforcement learning (RL). This paper quantifies
theoretically to what extent this extra information reduces RL's sample
complexity. In particular, we study the demonstration-regularized reinforcement
learning that leverages the expert demonstrations by KL-regularization for a
policy learned by behavior cloning. Our findings reveal that using
$N^{\mathrm{E}}$ expert demonstrations enables the identification of an optimal
policy at a sample complexity of order
$\widetilde{O}(\mathrm{Poly}(S,A,H)/(\varepsilon^2 N^{\mathrm{E}}))$ in finite
and $\widetilde{O}(\mathrm{Poly}(d,H)/(\varepsilon^2 N^{\mathrm{E}}))$ in
linear Markov decision processes, where $\varepsilon$ is the target precision,
$H$ the horizon, $A$ the number of action, $S$ the number of states in the
finite case and $d$ the dimension of the feature space in the linear case. As a
by-product, we provide tight convergence guarantees for the behaviour cloning
procedure under general assumptions on the policy classes. Additionally, we
establish that demonstration-regularized methods are provably efficient for
reinforcement learning from human feedback (RLHF). In this respect, we provide
theoretical evidence showing the benefits of KL-regularization for RLHF in
tabular and linear MDPs. Interestingly, we avoid pessimism injection by
employing computationally feasible regularization to handle reward estimation
uncertainty, thus setting our approach apart from the prior works.
