Title: Learning Policies for Markov Decision Processes from Data,
Abstract: We consider the problem of learning a policy for a Markov decision process
consistent with data captured on the state-actions pairs followed by the
policy. We assume that the policy belongs to a class of parameterized policies
which are defined using features associated with the state-action pairs. The
features are known a priori, however, only an unknown subset of them could be
relevant. The policy parameters that correspond to an observed target policy
are recovered using $\ell_1$-regularized logistic regression that best fits the
observed state-action samples. We establish bounds on the difference between
the average reward of the estimated and the original policy (regret) in terms
of the generalization error and the ergodic coefficient of the underlying
Markov chain. To that end, we combine sample complexity theory and sensitivity
analysis of the stationary distribution of Markov chains. Our analysis suggests
that to achieve regret within order $O(\sqrt{\epsilon})$, it suffices to use
training sample size on the order of $\Omega(\log n \cdot poly(1/\epsilon))$,
where $n$ is the number of the features. We demonstrate the effectiveness of
our method on a synthetic robot navigation example.