I wanted to leave a comment to respond to your comment about the “rationality” of minimax-Q, but comments are closed at http://thesilog.sologen.net/?p=76, so I decided to leave my comment here.

The “non-rationality” of minimax-Q follows from Bowling and Veloso’s (idiosyncratic?) definition of rationality. Specifically, they define it to be converging to best response against a stationary strategy (even a suboptimal one). Minimax-Q actually ignores the opponent’s strategy and assumes a worst-case opponent, so, indeed minimax-Q fails to satisfy their definition.

Your alternative definition is interesting. It says that a “rational” learning algorithm should adopt a best response to any Nash-equilibrium opponent. In zero-sum games (which is where minimax-Q makes the most sense), this definition is equivalent to saying that the learner should adopt a minimax policy. Of course, that’s exactly what minimax-Q does, so it passes your rationality test in this case.

-Michael