Imitation Learning in Discounted Linear MDPs without exploration assumptions

We present a new algorithm for imitation learning in infinite horizon linear MDPs dubbed ILARL which greatly improves the bound on the number of trajectories that the learner needs to sample from the environment. In particular, we re- move exploration assumptions required in previous works and we improve the dependence on the desired accuracy ε from Oε−5to Oε−4. Our result relies on a connection between imitation earning and online learning in MDPs with adversarial losses. For the latter setting, we present the first result for infinite horizon linear MDP which may be of independent interest. Moreover, we are able to provide a strengthen result for the finite horizon case where we achieve Oε−2. Numerical experiments with linear function ap-proximation shows that ILARL outperforms other commonly used algorithms.