Inverse reinforcement learning (IRL) is the problem of learning the preferences of an agent from the observations of its behavior on a task. While this problem has been well investigated, the related problem of {em online} IRL---where the observations are incrementally accrued, yet the demands of the application often prohibit a full rerun of an IRL method---has received relatively less attention. We introduce the first formal framework for online IRL, called incremental IRL (I2RL), and a new method that advances maximum entropy IRL with hidden variables, to this setting. Our formal analysis shows that the new method has a monotonically improving performance with more demonstration data, as well as probabilistically bounded error, both under full and partial observability. Experiments in a simulated robotic application of penetrating a continuous patrol under occlusion shows the relatively improved performance and speed up of the new method and validates the utility of online IRL.
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