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IRL as I understand is where the AI is given a policy from an "expert" and needs to solve for the reward function which best fits the policy.

And Apprenticeship Learning via IRL was explained as an expert demonstrating a skill and the reward function also has to be derived using the expert behavior.

I don't necessarily understand the difference between the two since apprenticeship learning directly uses IRL. Any explanation of differences would be helpful.

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Apprenticeship Learning uses Inverse Reinforcement Learning and there is a subtle difference between the two. Inverse Reinforcement Learning tries to recover the reward function ($R^*$) from demonstration trace of a teacher (an expert at the task being solved). Finding the optimal policy ($\pi^*$) from that "guessed" reward is what is meant by Apprenticeship Learning. More information on this link.

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