I don’t suppose you could clarify what the unresolved issues in decision theory are. What are the biggest issues that haven’t been solved for UDT or FDT? What is a co-ordination problem that hasn’t been solved? And what still isn’t known about counterfactuals?
What are the biggest issues that haven’t been solved for UDT or FDT?
UDT was a fairly simple and workable idea in classical Bayesian settings with logical omniscience (or with some simple logical uncertainty treated as if it were empirical uncertainty), but it was always intended to utilize logical uncertainty at its core. Logical induction, our current-best theory of logical uncertainty, doesn’t turn out to work very well with UDT so far. The basic problem seems to be that UDT required “updates” to be represented in a fairly explicit way: you have a prior which already contains all the potential things you can learn, and an update is just selecting certain possibilities. Logical induction, in contrast, starts out “really ignorant” and adds structure, not just content, to its beliefs over time. Optimizing via the early beliefs doesn’t look like a very good option, as a result.
FDT requires a notion of logical causality, which hasn’t appeared yet.
What is a co-ordination problem that hasn’t been solved?
Taking logical uncertainty into account, all games become iterated games in a significant sense, because players can reason about each other by looking at what happens in very close situations. If the players have T seconds to think, they can simulate the same game but given t<<T time to think, for many t. So, they can learn from the sequence of “smaller” games.
This might seem like a good thing. For example, single-shot prisoner’s dilemma has just a Nash equilibrium of defection. Iterated play cas cooperative equilibria, such as tit-for-tat.
Unfortunately, the folk theorem of game theory implies that there are a whole lot of fairly bad equilibria for iterated games as well. It is possible that each player enforces a cooperative equilibrium via tit-for-tat-like strategies. However, it is just as possible for players to end up in a mutual blackmail double bind, as follows:
Both players initially have some suspicion that the other player is following strategy X: “cooperate 1% of the time if and only if the other player is playing consistently with strategy X; otherwise, defect 100% of the time.” As a result of this suspicion, both players play via strategy X in order to get the 1% cooperation rather than 0%.
Ridiculously bad “coordination” like that can be avoided via cooperative oracles, but that requires everyone to somehow have access to such a thing. Distributed oracles are more realistic in that each player can compute them just by reasoning about the others, but players using distributed oracles can be exploited.
So, how do you avoid supremely bad coordination in a way which isn’t too badly exploitable?
And what still isn’t known about counterfactuals?
The problem of specifying good counterfactuals sort of wraps up any and all other problems of decision theory into itself, which makes this a bit hard to answer. Different potential decision theories may lean more or less heavily on the counterfactuals. If you lead toward EDT-like decision theories, the problem with counterfactuals is mostly just the problem of making UDT-like solutions work. For CDT-like decision theories, it is the other way around; the problem of getting UDT to work is mostly about getting the right counterfactuals!
The mutual-blackmail problem I mentioned in my “coordination” answer is a good motivating example. How do you ensure that the agents don’t come to think “I have to play strategy X, because if I don’t, the other player will cooperate 0% of the time?”
I don’t suppose you could clarify what the unresolved issues in decision theory are. What are the biggest issues that haven’t been solved for UDT or FDT? What is a co-ordination problem that hasn’t been solved? And what still isn’t known about counterfactuals?
UDT was a fairly simple and workable idea in classical Bayesian settings with logical omniscience (or with some simple logical uncertainty treated as if it were empirical uncertainty), but it was always intended to utilize logical uncertainty at its core. Logical induction, our current-best theory of logical uncertainty, doesn’t turn out to work very well with UDT so far. The basic problem seems to be that UDT required “updates” to be represented in a fairly explicit way: you have a prior which already contains all the potential things you can learn, and an update is just selecting certain possibilities. Logical induction, in contrast, starts out “really ignorant” and adds structure, not just content, to its beliefs over time. Optimizing via the early beliefs doesn’t look like a very good option, as a result.
FDT requires a notion of logical causality, which hasn’t appeared yet.
Taking logical uncertainty into account, all games become iterated games in a significant sense, because players can reason about each other by looking at what happens in very close situations. If the players have T seconds to think, they can simulate the same game but given t<<T time to think, for many t. So, they can learn from the sequence of “smaller” games.
This might seem like a good thing. For example, single-shot prisoner’s dilemma has just a Nash equilibrium of defection. Iterated play cas cooperative equilibria, such as tit-for-tat.
Unfortunately, the folk theorem of game theory implies that there are a whole lot of fairly bad equilibria for iterated games as well. It is possible that each player enforces a cooperative equilibrium via tit-for-tat-like strategies. However, it is just as possible for players to end up in a mutual blackmail double bind, as follows:
Both players initially have some suspicion that the other player is following strategy X: “cooperate 1% of the time if and only if the other player is playing consistently with strategy X; otherwise, defect 100% of the time.” As a result of this suspicion, both players play via strategy X in order to get the 1% cooperation rather than 0%.
Ridiculously bad “coordination” like that can be avoided via cooperative oracles, but that requires everyone to somehow have access to such a thing. Distributed oracles are more realistic in that each player can compute them just by reasoning about the others, but players using distributed oracles can be exploited.
So, how do you avoid supremely bad coordination in a way which isn’t too badly exploitable?
The problem of specifying good counterfactuals sort of wraps up any and all other problems of decision theory into itself, which makes this a bit hard to answer. Different potential decision theories may lean more or less heavily on the counterfactuals. If you lead toward EDT-like decision theories, the problem with counterfactuals is mostly just the problem of making UDT-like solutions work. For CDT-like decision theories, it is the other way around; the problem of getting UDT to work is mostly about getting the right counterfactuals!
The mutual-blackmail problem I mentioned in my “coordination” answer is a good motivating example. How do you ensure that the agents don’t come to think “I have to play strategy X, because if I don’t, the other player will cooperate 0% of the time?”
I second that request.