Imitation Learning in Discounted Linear MDP without exploration assumptions

Luca Viano, Stratis Skoulakis, Volkan Cevher

Keywords: imitation learning theory

TL;DR: improved bounds for the MDP trajectory complexity in discounted linear MDP

Abstract:

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 remove exploration assumptions required in previous works and we improve the dependence on the desired accuracy $\epsilon$ from $\mathcal{O}\br{\epsilon^{-5}}$ to $\mathcal{O}\br{\epsilon^{-4}}$.
Our result relies on a connection between imitation learning 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 $\mathcal{O}\br{\epsilon^{-2}}$. Numerical experiments with linear function approximation shows that ILARL outperforms other commonly used algorithms.

Already Accepted Paper At Another Venue: already accepted somewhere else

Submission Number: 35