It seems to me that how to combine utility functions follows from how you then choose an action.
Let’s say we have 10 hypotheses and we maximize utility. We can afford to let each hypothesis rule out up to a tenth of the action space as extremely negative in utility, but we can’t let a hypothesis assign extremely positive utility to any action. Therefore we sample about 9 random actions (which partition action space into 10 pieces) and translate the worst of them to 0, then scale the maximum over all actions to 1. (Or perhaps, we set the 10th percentile to 0 and the hundredth to 1.)
Let’s say we have 10 hypotheses and we sample a random action from the top half. Then, by analogous reasoning, we sample 19 actions, normalize the worst to 0 and the best to 1. (Or perhaps set the 5th to 0 and the 95th to 1. Though then it might devolve into a fight over who can think of the largest/smallest number on the fringes...)
It seems to me that how to combine utility functions follows from how you then choose an action.
Let’s say we have 10 hypotheses and we maximize utility. We can afford to let each hypothesis rule out up to a tenth of the action space as extremely negative in utility, but we can’t let a hypothesis assign extremely positive utility to any action. Therefore we sample about 9 random actions (which partition action space into 10 pieces) and translate the worst of them to 0, then scale the maximum over all actions to 1. (Or perhaps, we set the 10th percentile to 0 and the hundredth to 1.)
Let’s say we have 10 hypotheses and we sample a random action from the top half. Then, by analogous reasoning, we sample 19 actions, normalize the worst to 0 and the best to 1. (Or perhaps set the 5th to 0 and the 95th to 1. Though then it might devolve into a fight over who can think of the largest/smallest number on the fringes...)
The general principle is giving the daemon as much slack/power as possible while bounding our proxy of its power.