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 @math -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 @math , it suffices to use training sample size on the order of @math , where @math is the number of the features. We demonstrate the effectiveness of our method on a synthetic robot navigation example.
There is substantial work in the literature on learning MDP policies by observing experts; see @cite_17 for a survey. We next discuss papers that are more closely related to our work.
@cite_17
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We present a comprehensive survey of robot Learning from Demonstration (LfD), a technique that develops policies from example state to action mappings. We introduce the LfD design choices in terms of demonstrator, problem space, policy derivation and performance, and contribute the foundations for a structure in which to categorize LfD research. Specifically, we analyze and categorize the multiple ways in which examples are gathered, ranging from teleoperation to imitation, as well as the various techniques for policy derivation, including matching functions, dynamics models and plans. To conclude we discuss LfD limitations and related promising areas for future research.