Timeless decision theory (TDT) is a decision theory developed by Eliezer Yudkowsky which, in slogan form, says that agents should decide as if they are determining the output of the abstract computation that they implement. This theory was developed in response to the view that rationality should be about winning (that is, about agents achieving their desired ends) rather than about behaving in a manner that we would intuitively label as rational. Prominent existing decision theories (including causal decision theory, or CDT) fail to choose the winning decision in some scenarios and so there is a need to develop a more successful theory.

Timeless Decision Theory has been replaced by Functional Decision Theory

In response to some of Eliezer's writing on TDT, Wei Dai came up with Updateless Decision Theory (UDT). UDT is clearly superior to TDT in cases such as counterfactual mugging. TDT gets these problems wrong as a result of updating on its observations before calculating expected utility; even though it is considering the consequences of its policies in the abstract, it is doing so only in the "current branch" (ie, updatefully), and so it misses the positive consequences of its policy on other branches.

Functional decision theory (FDT) was an attempt to write up the general motivation behind both TDT and UDT in a more general way, which would have ideally created an umbrella term for decision theories sharing a flavor with UDT and TDT. To this end, the coathors of the FDT paper attempted to include Wei Dai as a coathor and get his approval of the general write-up as representing the spirit of UDT. However, the direction of the paper ended up heavily incorporating intuitions from causal decision theory (CDT), describing FDT as a shift from physical causality to logical causality, so that abstract mathematical nodes such as (critically) the output of the decision procedure could be included in the causal picture, and understood as exercising causal influence, even over physical circumstances.

Wei Dai intended UDT to be much closer to evidential decision theory (EDT) and further from CDT in spirit, and as such, declined to co-author the paper.

The FDT paper thus describes a general framework which remains agnostic about an updateless approach (like UDT) vs an updateful one (like TDT), but which sticks close to the logical-causality approach introduced by TDT. As such, it can be regarded as a successor to TDT (because it backs off from the fundamental mistake of TDT, namely, its updatefulness, while sticking to the core logical-causality intuition of TDT).

TDT and Newcomb's problem

A better sense of the motivations behind, and form of, TDT can be gained by considering a particular decision scenario: Newcomb's problem. In Newcomb's problem, a superintelligent artificial intelligence, Omega, presents you with a transparent box and an opaque box. The transparent box contains $1000 while the opaque box contains either $1,000,000 or nothing. You are given the choice to either take both boxes (called two-boxing) or just the opaque box (one-boxing). However, things are complicated by the fact that Omega is an almost perfect predictor of human behavior and has filled the opaque box as follows: if Omega predicted that you would one-box, it filled the box with $1,000,000 whereas if Omega predicted that you would two-box it filled it with nothing.

Many people find it intuitive that it is rational to two-box in this case. As the opaque box is already filled, you cannot influence its contents with your decision so you may as well take both boxes and gain the extra $1000 from the transparent box. CDT formalizes this style of reasoning. However, one-boxers win in this scenario. After all, if you one-box then Omega (almost certainly) predicted that you would do so and hence filled the opaque box with $1,000,000. So you will almost certainly end up with $1,000,000 if you one-box. On the other hand, if you two-box, Omega (almost certainly) predicted this and so left the opaque box empty . So you will almost certainly end up with $1000 (from the transparent box) if you two-box. Consequently, if rationality is about winning then it's rational to one-box in Newcomb's problem (and hence CDT fails to be an adequate decision theory).

TDT will endorse one-boxing in this scenario and hence endorses the winning decision. When Omega predicts your behavior, it carries out the same abstract computation as you do when you decide whether to one-box or two-box. To make this point clear, we can imagine that Omega makes this prediction by creating a simulation of you and observing its behavior in Newcomb's problem. This simulation will clearly decide according to the same abstract computation as you do as both you and it decide in the same manner. Now, given that TDT says to act as if deciding the output of this computation, it tells you to act as if your decision to one-box can determine the behavior of the simulation (or, more generally, Omega's prediction) and hence the filling of the boxes. So TDT correctly endorses one-boxing in Newcomb's problem as it tells the agent to act as if doing so will lead them to get $1,000,000 instead of $1,000.

TDT and other decision scenarios

TDT also wins in a range of other cases including medical Newcomb's problems, Parfit's hitchhiker, and the one-shot prisoners' dilemma. However, there are other scenarios where TDT does not win, including counterfactual mugging. This suggests that TDT still requires further development if it is to become a fully adequate decision theory. Given this, there is some motivation to also consider alternative decision theories alongside TDT, like updateless decision theory (UDT), which also wins in a range of scenarios but has its own problem cases. It seems likely that both of these theories draw on insights which are crucial to progressing our understanding of decision theory. So while TDT requires further development to be entirely adequate, it nevertheless represents a substantial step toward developing a decision theory that always endorses the winning decision

Formalization of TDT

Coming to fully grasp TDT requires an understanding of how the theory is formalized. Very briefly, TDT is formalized by supplementing causal Bayesian networks, which can be thought of as graphs representing causal relations, in two ways. First, these graphs should be supplemented with nodes representing abstract computations and an agent's uncertainty about the result of these computations. Such a node might represent an agent's uncertainty about the result of a mathematical sum. Second, TDT treats decisions as the abstract computation that underlies the agent's decision process. These two features transform causal Bayesian networks into timeless decision diagrams. Using these supplemented diagrams, TDT is able to determine the winning decision in a whole range of a decision scenarios. For a more detailed description of the formalization of TDT, see Eliezer Yudkowsky's timeless decision theory paper.

Further Reading

A Comparison of Decision Algorithms on Newcomblike Problems, by Alex Altair
Problem Class Dominance in Predictive Dilemmas, by Danny Hintze

Notable Posts

Ingredients of Timeless Decision Theory
Timeless Decision Theory: Problems I Can't Solve
Timeless Decision Theory and Meta-Circular Decision Theory
Decision theory: Why Pearl helps reduce "could" and "would", but still leaves us with at least three alternatives by Anna Salamon

External Links

Timeless Decision Theory (2010) by Eliezer Yudkowsky
An Introduction to Timeless Decision Theory at Formalised Thinking

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