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Up­date­less De­ci­sion Theory

TagLast edit: 25 Jun 2022 22:34 UTC by Thomas Larsen

Motivation

Updateless Decision Theory (UDT) is a decision theory meant to deal with a fundamental problem in the existing decision theories: the need to treat the agent as a part of the world in which it makes its decisions. In contrast, in the most common decision theory today, Causal Decision Theory (CDT), the deciding agent is not part of the world model—its decision is the output of the CDT, but the agent’s decision in the world context is “magic”: in the moment of deciding, no causal links feed into its chosen action. It acts as though its decision was causeless, as in some dualist free-will theories.

Getting this issue right is critical in building a self-improving artificial general intelligence, as such an AI must analyze its own behavior and that of a next generation that it may build.

Updateless Decision Theory was invented by Wei Dai and first described in Towards a New Decision Theory.

See also

Content

UDT specifies that the optimal agent is the one with the best algorithm—the best mapping from observations to actions—across a probability distribution of all world-histories. (“Best” here, as in other decision theories, means one that maximizes a utility/​reward function.)

This definition may seem trivial, but in contrast, CDT says that an agent should choose the best *option* at any given moment, based on the effects of that action. As in Judea Pearl’s definition of causality, CDT ignores any causal links inbound to the decider, treating this agent as an uncaused cause. The agent is unconcerned about what evidence its decision may provide about the agent’s own mental makeup—evidence which may suggest that the agent will make suboptimal decisions in other cases.

Evidential Decision Theory is the other leading decision theory today. It says that the agent should make the choice for which the expected utility, as calculated with Bayes’ Rule, is the highest. EDT avoids CDT’s pitfalls, but has its own flaw: It ignores the distinction between causation and correlation. In CDT, the agent is an uncaused cause, and in EDT, the converse: It is caused, but not a cause.

One valuable insight from EDT is reflected in “UDT 1.1” (see article by McAllister in references), a variant of UDT in which the agent takes into account that some of its algorithm (mapping from observations to actions) may be prespecified and not entirely in its control, so that it has to gather evidence and draw conclusions about part of its own mental makeup. The difference between UDT 1.0 and 1.1 is that UDT 1.1 iterates over policies, whereas UDT 1.0 iterates over actions.

Both UDT and Timeless Decision Theory (TDT) make decisions on the basis of what you would have pre-committed to. The difference is that UDT asks what you would have pre-committed to without the benefit of any observations you have made about the universe, while TDT asks what you would have pre-committed to give all information you’ve observed so far. This means that UDT pays in Counterfactual Mugging, while TDT does not.

UDT is very similar to Functional Decision Theory (FDT), but there are differences. FDT doesn’t include the UDT1.1 fix and Nate Soares states: “Wei Dai doesn’t endorse FDT’s focus on causal-graph-style counterpossible reasoning; IIRC he’s holding out for an approach to counterpossible reasoning that falls out of evidential-style conditioning on a logically uncertain distribution”. Rob Bensinger says that he’s heard UDT described as “FDT + a theory of anthropics”.

Since it is formalised using input-output maps instead of in terms of situations, it allows us to make predictions about what an agent would do given input representing an inconsistent situation, which can be important when dealing with perfect predictors.

Logical Uncertainty

A robust theory of logical uncertainty is essential to a full formalization of UDT. A UDT agent must calculate probabilities and expected values on the outcome of its possible actions in all possible worlds—sequences of observations and its own actions. However, it does not know its own actions in all possible worlds. (The whole point is to derive its actions.) On the other hand, it does have some knowledge about its actions, just as you know that you are unlikely to walk straight into a wall the next chance you get. So, the UDT agent models itself as an algorithm, and its probability distribution about what it itself will do is an important input into its maximization calculation.

Logical uncertainty is an area which has not yet been properly formalized, and much UDT research is focused on this area.

Blog posts

Relevant Comments

In addition to whole posts on UDT, there are also a number of comments which contain important information, often on less relevant posts.

External links

Towards a New De­ci­sion Theory

Wei_Dai13 Aug 2009 5:31 UTC
79 points
146 comments6 min readLW link

A Short Note on UDT

Chris_Leong8 Aug 2018 13:27 UTC
10 points
9 comments1 min readLW link

UDT as a Nash Equilibrium

cousin_it6 Feb 2018 14:08 UTC
18 points
17 comments1 min readLW link

“UDT2” and “against UD+ASSA”

Wei_Dai12 May 2019 4:18 UTC
49 points
7 comments7 min readLW link

Up­date­less­ness and Son of X

Scott Garrabrant4 Nov 2016 22:58 UTC
11 points
0 comments3 min readLW link

UDT can learn an­thropic probabilities

cousin_it24 Jun 2018 18:04 UTC
54 points
10 comments3 min readLW link

Tor­ture vs. Dust vs. the Pre­sump­tu­ous Philoso­pher: An­thropic Rea­son­ing in UDT

Wei_Dai3 Sep 2009 23:04 UTC
32 points
29 comments2 min readLW link

The Ab­sent-Minded Driver

Wei_Dai16 Sep 2009 0:51 UTC
43 points
150 comments3 min readLW link

Why (and why not) Bayesian Up­dat­ing?

Wei_Dai16 Nov 2009 21:27 UTC
26 points
26 comments2 min readLW link

What Are Prob­a­bil­ities, Any­way?

Wei_Dai11 Dec 2009 0:25 UTC
40 points
89 comments2 min readLW link

Ex­plicit Op­ti­miza­tion of Global Strat­egy (Fix­ing a Bug in UDT1)

Wei_Dai19 Feb 2010 1:30 UTC
55 points
38 comments2 min readLW link

List of Prob­lems That Mo­ti­vated UDT

Wei_Dai6 Jun 2012 0:26 UTC
42 points
11 comments1 min readLW link

Another at­tempt to ex­plain UDT

cousin_it14 Nov 2010 16:52 UTC
58 points
54 comments2 min readLW link

What is Wei Dai’s Up­date­less De­ci­sion The­ory?

AlephNeil19 May 2010 10:16 UTC
54 points
67 comments7 min readLW link

Con­cep­tual Prob­lems with UDT and Policy Selection

abramdemski28 Jun 2019 23:50 UTC
59 points
16 comments9 min readLW link

An im­ple­men­ta­tion of modal UDT

Benya_Fallenstein11 Feb 2015 6:02 UTC
8 points
0 comments1 min readLW link

Un­der­stand­ing up­date­less­ness in the con­text of EDT and CDT

Sylvester Kollin5 Jul 2022 23:05 UTC
23 points
2 comments7 min readLW link