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Coherence implies mutual information between actions. That is, to be coherent, your actions can't be independent. This is true under several different definitions of coherence, and can be seen in the following circumstances:
When trading between resources (uncertainty over utility function). If you trade 3 apples for 2 bananas, this is information that you won't trade 3 bananas for 2 apples, if there's some prior distribution over your utility function.
When taking multiple actions from the same utility function (uncertainty over utility function). Your actions will all have to act like a phased array pushing the variables you care about in some direction.
When taking multiple actions based on the same observation (uncertainty over observation / world-state). Suppose that you're trying to juggle, and your vision is either reversed or not reversed. The actions of your left arm and right arm will have mutual information, because they both depend on whether your vision has been reversed in related ways.
This would be a full post, but I don't think it's important enough to write up.
Your actions will all have to act like a phased array pushing the variables you care about in some direction.
The nice thing is that this should work even if you are a policy selected by a decision making algorithm, but you are not yourself a decision making algorithm anymore. There is no preference in any of the possible runs of the policy at that point, you don't care about anything now, you only know what you must do here, and not elsewhere. But if all possible runs of the policy are considered altogether (in the updateless sense of maps from epistemi... (read more)