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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In this paper we address the problem of learning a policy from demonstration. Assuming that the policy to be learned is the optimal policy for an underlying MDP, we propose a novel way of leveraging the underlying MDP structure in a kernel-based approach. Our proposed approach rests on the insight that the MDP structure can be encapsulated into an adequate state-space metric. In particular we show that, using MDP metrics, we are able to cast the problem of learning from demonstration as a classification problem and attain similar generalization performance as methods based on inverse reinforcement learning at a much lower online computational cost. Our method is also able to attain superior generalization than other supervised learning methods that fail to consider the MDP structure. A popular approach for online decision making in large MDPs is time-bounded tree search. The effectiveness of tree search, however, is largely influenced by the action branching factor, which limits the search depth given a time bound. An obvious way to reduce action branching is to consider only a subset of potentially good actions at each state as specified by a provided partial policy. In this work, we consider offline learning of such partial policies with the goal of speeding up search without significantly reducing decision-making quality. Our first contribution is to study learning algorithms based on reducing our learning problem to i.i.d. supervised learning. We give a reduction-style analysis of three such algorithms, each making different assumptions, which relates the supervised learning objectives to the sub-optimality of search using the learned partial policies. Our second contribution is to describe concrete implementations of the algorithms within the popular framework of Monte-Carlo tree search. Finally, the third contribution is to evaluate the learning algorithms in two challenging MDPs with large action branching factors, showing that the learned partial policies can significantly improve the anytime performance of Monte-Carlo tree search. We consider the problem of imitation learning where the examples, demonstrated by an expert, cover only a small part of a large state space. Inverse Reinforcement Learning (IRL) provides an ecient tool for generalizing the demonstration, based on the assumption that the expert is optimally acting in a Markov Decision Process (MDP). Most of the past work on IRL requires that a (near)optimal policy can be computed for dierent reward functions. However, this requirement can hardly be satised in systems with a large, or continuous, state space. In this paper, we propose a model-free IRL algorithm, where the relative entropy between the empirical distribution of the state-action trajectories under a baseline policy and their distribution under the learned policy is minimized by stochastic gradient descent. We compare this new approach to well-known IRL algorithms using learned MDP models. Empirical results on simulated car racing, gridworld and ball-in-a-cup problems show that our approach is able to learn good policies from a small number of demonstrations. In apprenticeship learning, the goal is to learn a policy in a Markov decision process that is at least as good as a policy demonstrated by an expert. The difficulty arises in that the MDP's true reward function is assumed to be unknown. We show how to frame apprenticeship learning as a linear programming problem, and show that using an off-the-shelf LP solver to solve this problem results in a substantial improvement in running time over existing methods---up to two orders of magnitude faster in our experiments. Additionally, our approach produces stationary policies, while all existing methods for apprenticeship learning output policies that are "mixed", i.e. randomized combinations of stationary policies. The technique used is general enough to convert any mixed policy to a stationary policy.