But then it seems to me that Game 3 is unfair, in that it artificially amplifies infinitesimal errors. Faced with a hostile input, a Solomonoff predictor will correctly converge to saying “I don’t know,” i.e. producing p(0) ~ p(1) ~ 1⁄2. However, a game that forces it to nevertheless make binary predictions in this situation will force an answer based on the infinitesimal differences between the calculated probabilities and 1⁄2, and moreover, the correct answers are contrived so that these infinitesimal differences always point in the wrong direction.
If you instead let the Solomonoff predictor just honestly say “I don’t know,” as in the first two games, the problem disappears.
If you instead let the Solomonoff predictor just honestly say “I don’t know,” as in the first two games, the problem disappears.
True, though sometimes in real life, you can’t just say “I don’t know”, you have to choose an action. Game 3 is unfair, but real life can be unfair too.
But then it seems to me that Game 3 is unfair, in that it artificially amplifies infinitesimal errors. Faced with a hostile input, a Solomonoff predictor will correctly converge to saying “I don’t know,” i.e. producing p(0) ~ p(1) ~ 1⁄2. However, a game that forces it to nevertheless make binary predictions in this situation will force an answer based on the infinitesimal differences between the calculated probabilities and 1⁄2, and moreover, the correct answers are contrived so that these infinitesimal differences always point in the wrong direction.
If you instead let the Solomonoff predictor just honestly say “I don’t know,” as in the first two games, the problem disappears.
True, though sometimes in real life, you can’t just say “I don’t know”, you have to choose an action. Game 3 is unfair, but real life can be unfair too.