One sufficient condition for always defining actions is when a decision theory can give decisions as a function of the state of the world. For example, CDT evaluates outcomes in a way purely dependent on the world’s state. A more complicated way of doing this is if your decision theory takes in a model of the world and outputs a policy, which tells you what to do in each state of the world.
As a clarification, I’m considering the case where we consider the state space to be the set of all “possible” histories (including counter-logical ones), like the standard “general RL” (i.e. AIXI-style) set-up.
Well, maybe I didn’t do a good job understanding your question :)
Decision procedures that don’t return an answer, or that fail to halt, for some of the “possible” histories, seem like a pretty broad category. Ditto for decision procedures that always have an answer.
But I guess a lot of those decision procedures are boring or dumb. So maybe you were thinking about a question like “for sufficiently ‘good’ decision theories, do they all end up specifying responses for all counter-logical histories, or do they leave free parameters?”
One sufficient condition for always defining actions is when a decision theory can give decisions as a function of the state of the world. For example, CDT evaluates outcomes in a way purely dependent on the world’s state. A more complicated way of doing this is if your decision theory takes in a model of the world and outputs a policy, which tells you what to do in each state of the world.
I don’t understand how this answers the question.
As a clarification, I’m considering the case where we consider the state space to be the set of all “possible” histories (including counter-logical ones), like the standard “general RL” (i.e. AIXI-style) set-up.
Well, maybe I didn’t do a good job understanding your question :)
Decision procedures that don’t return an answer, or that fail to halt, for some of the “possible” histories, seem like a pretty broad category. Ditto for decision procedures that always have an answer.
But I guess a lot of those decision procedures are boring or dumb. So maybe you were thinking about a question like “for sufficiently ‘good’ decision theories, do they all end up specifying responses for all counter-logical histories, or do they leave free parameters?”
Am I on the right track?