Demonstration-Regularized RL
Daniil Tiapkin Denis Belomestny Daniele Calandriello Eric Moulines Alexey Naumov Pierre Perrault Michal Valko Pierre Menard
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
$\widetilde{\mathcal{O}}(\mathrm{Poly}(S,A,H)/(\varepsilon^2 N^{\mathrm{E}}))$
in finite and $\widetilde{\mathcal{O}}(\mathrm{Poly}(d,H)/(\varepsilon^2
N^{\mathrm{E}}))$ 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.