  Inverse reinforcement learning (IRL) is the task of finding a reward function
that generates a desired optimal policy for a given Markov Decision Process
(MDP). This paper develops an information-theoretic lower bound for the sample
complexity of the finite state, finite action IRL problem. A geometric
construction of $\beta$-strict separable IRL problems using spherical codes is
considered. Properties of the ensemble size as well as the Kullback-Leibler
divergence between the generated trajectories are derived. The resulting
ensemble is then used along with Fano's inequality to derive a sample
complexity lower bound of $O(n \log n)$, where $n$ is the number of states in
the MDP.
