Inverse reinforcement learning (IRL) is the problem of finding a reward function that generates a given optimal policy for a given Markov Decision Process. This paper looks at an algorithmic-independent geometric analysis of the IRL problem with finite states and actions. A L1-regularized Support Vector Machine formulation of the IRL problem motivated by the geometric analysis is then proposed with the basic objective of the inverse reinforcement problem in mind: to find a reward function that generates a specified optimal policy. The paper further analyzes the proposed formulation of inverse reinforcement learning with n states and k actions, and shows a sample complexity of O(d~2 log(nk)) for transition probability matrices with at most d nonzeros per row, for recovering a reward function that generates a policy that satisfies Bellman's optimality condition with respect to the true transition probabilities.
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