How about if we restrict attention to games where at any stage the players are allowed to choose a probability distribution over the set of available moves, rather than being forced to choose one move? Is it then possible for Solomonoff induction to lose (whatever ‘lose’ means) with non-zero probability, in the limit?
In other words, does Solomonoff induction win all variants of game 1 that use different proper scoring rules in place of log score? Nice question. I’m going to sleep, will try to solve it tomorrow unless someone else does it first.
How about if we restrict attention to games where at any stage the players are allowed to choose a probability distribution over the set of available moves, rather than being forced to choose one move? Is it then possible for Solomonoff induction to lose (whatever ‘lose’ means) with non-zero probability, in the limit?
In other words, does Solomonoff induction win all variants of game 1 that use different proper scoring rules in place of log score? Nice question. I’m going to sleep, will try to solve it tomorrow unless someone else does it first.