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In other words, which existing reinforcement method learns with fewest episodes? R-Max comes to mind, but it's very old and I'd like to know if there is something better now.

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There isn't really one specific method which makes any RL agent have faster learning. Rather there is a long list of methods which have shown to increase the speed of learning and they can sometimes play nicely with each other.

Some examples:

  1. Options
  2. True Online Methods
  3. Asynchronous Methods

These are the most influential and promising methods I can think of but the list of techniques is not limited to these 3.

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There is a very interesting learning agent. They call it Neural-Episodic-Control. Here is the link for the paper: https://arxiv.org/abs/1703.01988 . Their experiments show that NEC requires an order of magnitude fewer interactions with the environment than agents previously proposed.

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