The first needs a lot of data and suffers from covariate shift. It’s a supervised learning method when we fit the state-action pair mapping. The latter finds a cost function under which the expert is uniquely optimal. Compounding error is not a problem here, but IRL is super data inefficiend and requires RL in the inner loop. Since we only interested in the final policy, why do we learn the cost function? So, GAIL was born.