  Various methods for solving the inverse reinforcement learning (IRL) problem
have been developed independently in machine learning and economics. In
particular, the method of Maximum Causal Entropy IRL is based on the
perspective of entropy maximization, while related advances in the field of
economics instead assume the existence of unobserved action shocks to explain
expert behavior (Nested Fixed Point Algorithm, Conditional Choice Probability
method, Nested Pseudo-Likelihood Algorithm). In this work, we make previously
unknown connections between these related methods from both fields. We achieve
this by showing that they all belong to a class of optimization problems,
characterized by a common form of the objective, the associated policy and the
objective gradient. We demonstrate key computational and algorithmic
differences which arise between the methods due to an approximation of the
optimal soft value function, and describe how this leads to more efficient
algorithms. Using insights which emerge from our study of this class of
optimization problems, we identify various problem scenarios and investigate
each method's suitability for these problems.
