Better Imitation Learning in Discounted Linear MDP

Luca Viano, Stratis Skoulakis, Volkan Cevher

Primary Area: reinforcement learning

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Keywords: imitation learning theory, online learning in MDP, reinforcement learning theory

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TL;DR: A new imitation learning algorithm with better guarantees for infinite horizon 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 $\mathcal{O}(\epsilon^{-5})$ to $\mathcal{O}(\epsilon^{-4})$.
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 $\mathcal{O}(\epsilon^{-2})$. Numerical experiments with linear function approximation shows that ILARL outperforms other commonly used algorithms.

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Submission Number: 673