  Inverse reinforcement learning (IRL) addresses the problem of recovering a
task description given a demonstration of the optimal policy used to solve such
a task. The optimal policy is usually provided by an expert or teacher, making
IRL specially suitable for the problem of apprenticeship learning. The task
description is encoded in the form of a reward function of a Markov decision
process (MDP). Several algorithms have been proposed to find the reward
function corresponding to a set of demonstrations. One of the algorithms that
has provided best results in different applications is a gradient method to
optimize a policy squared error criterion. On a parallel line of research,
other authors have presented recently a gradient approximation of the maximum
likelihood estimate of the reward signal. In general, both approaches
approximate the gradient estimate and the criteria at different stages to make
the algorithm tractable and efficient. In this work, we provide a detailed
description of the different methods to highlight differences in terms of
reward estimation, policy similarity and computational costs. We also provide
experimental results to evaluate the differences in performance of the methods.
