  Inverse reinforcement learning (IRL) is the problem of finding a reward
function that generates a given optimal policy for a given Markov Decision
Process. This paper looks at an algorithmic-independent geometric analysis of
the IRL problem with finite states and actions. A L1-regularized Support Vector
Machine formulation of the IRL problem motivated by the geometric analysis is
then proposed with the basic objective of the inverse reinforcement problem in
mind: to find a reward function that generates a specified optimal policy. The
paper further analyzes the proposed formulation of inverse reinforcement
learning with $n$ states and $k$ actions, and shows a sample complexity of
$O(n^2 \log (nk))$ for recovering a reward function that generates a policy
that satisfies Bellman's optimality condition with respect to the true
transition probabilities.
