It used to, as Tim notes, but I’m not so sure now. AIXI works with its distribution over programs and sequences of observations, not with states of a world and its properties. If presented with a sequence of observations generated by a program, it quickly figures out what the following observations are, but it’s more tricky here.
With other types of agents, we usually need to stipulate that the problem statement is somehow made clear to the agent. The way in which this could be achieved is not specified, and it seems very difficult to arrange through presenting an actual sequence of observations. So the shortcut is to draw the problem “directly” on agent’s mind in terms of agent’s ontology, and usually it’s possible in a moderately natural way. This all takes place apart from the agent observing the state of the coin.
However in case of AIXI, it’s not as clear how the elements of the problem setting should be expressed in terms of its ontology. Basically, we have two worlds corresponding to the different coin states, which could for simplicity be assumed to be generated by two programs. The first idea is to identify the programs generating these worlds with relevant AIXI’s hypotheses, so that observing “tails” excludes the “heads”-programs, and therefore the “heads”-world, from consideration.
But there are many possible “tails”-programs, and AIXI’s response depends on their distribution. For example, the choice of a particular “tails”-program could represent the state of other worlds. What does it say about this distribution that the problem statement was properly explained to the AIXI agent? It must necessarily be more than just observing “tails”, the same as for other types of agents (if you only toss a coin and it falls “tails”, this observation alone doesn’t incite me to pay up). Perhaps “tails”-programs that properly model CM also imply paying the mugger.
It used to, as Tim notes, but I’m not so sure now. AIXI works with its distribution over programs and sequences of observations, not with states of a world and its properties. If presented with a sequence of observations generated by a program, it quickly figures out what the following observations are, but it’s more tricky here.
With other types of agents, we usually need to stipulate that the problem statement is somehow made clear to the agent. The way in which this could be achieved is not specified, and it seems very difficult to arrange through presenting an actual sequence of observations. So the shortcut is to draw the problem “directly” on agent’s mind in terms of agent’s ontology, and usually it’s possible in a moderately natural way. This all takes place apart from the agent observing the state of the coin.
However in case of AIXI, it’s not as clear how the elements of the problem setting should be expressed in terms of its ontology. Basically, we have two worlds corresponding to the different coin states, which could for simplicity be assumed to be generated by two programs. The first idea is to identify the programs generating these worlds with relevant AIXI’s hypotheses, so that observing “tails” excludes the “heads”-programs, and therefore the “heads”-world, from consideration.
But there are many possible “tails”-programs, and AIXI’s response depends on their distribution. For example, the choice of a particular “tails”-program could represent the state of other worlds. What does it say about this distribution that the problem statement was properly explained to the AIXI agent? It must necessarily be more than just observing “tails”, the same as for other types of agents (if you only toss a coin and it falls “tails”, this observation alone doesn’t incite me to pay up). Perhaps “tails”-programs that properly model CM also imply paying the mugger.
I don’t understand. Isn’t the biggest missing piece (an) AIXI’s precise utility function, rather than its uncertainty?