Robust decision making in uncertain environments

Henry Brighton

Motivation

• Practically all cognitive tasks involve uncertainty:– E.g., vision, language, memory, learning, decision making.– Humans and other animals are well adapted to uncertain

environments.

• Artificial Intelligence (AI) considers the same tasks:– These problems appear to be computationally demanding. – “Every problem we look at in AI is NP-complete”

(Reddy, 1998).

• How do humans and other animals deal with uncertainty?– The study of simple heuristic mechanisms.– Robust responses to uncertainty via simplicity.

Catching a ball

When a man throws a ball high in the air and catches it again, he behaves as if he had solved a set of differential equations in predicting the trajectory of the ball... At some subconscious level, something functionally equivalent to the mathematical calculation is going on.

-- Richard Dawkins, The Selfish Gene

Gaze heuristicFix your gaze on the ball, start running,and adjust your running speed so that the angle of gaze remains constant.

Gaze heuristicFix your gaze on the ball, start running,and adjust your running speed so that the angle of gaze remains constant.

Gaze heuristicFix your gaze on the ball, start running,and adjust your running speed so that the angle of gaze remains constant.

Gaze heuristicFix your gaze on the ball, start running,and adjust your running speed so that the angle of gaze remains constant.

• Bats, birds, and dragonflies maintain a constant optical angle between themselves and their prey.

• Dogs do the same, when catching a Frisbee (Shaffer et al., 2004).

• Ignore: velocity, angle, air resistance, speed, direction of wind, and spin.

Heuristics ignore information

Peahen mate choice (Petrie & Halliday, 1994).

?

Heuristic strategies are:• Computationally efficient, consuming few resources.• Ignore information, and seek “good enough” solutions.• Many examples in biology, termed “rules of thumb”.

Why use heuristics?

CostAccuracy

Effort

The accuracy-effort trade-off

• Information search and computation cost time and effort.• Therefore, minds rely on simple heuristics that are less accurate than

strategies that use more information and computation. • This view is widely held within cognitive science, economics, and beyond.

The study of heuristics

More information or computation can decrease accuracy; therefore, minds rely on simple heuristics in order to be more accurate than strategies that use more information and time.

Heuristics as functional responses to environmental uncertainty.

Three widely held assumptions:

1. Heuristics are always second-best.2. We use heuristics only because of our cognitive limitations.3. More information, more computation, and more time would always be better.

A stronger hypothesis, the possibility that less-is-more:

City Population Soccer team?

State capital?

Former GDR?

Industrial belt?

License letter?

Intercity train-line?

Expo site?

National capital?

University?

Berlin 3,433,695 No Yes No No Yes Yes Yes Yes Yes

Hamburg 1,652,363 Yes Yes No No No Yes Yes No Yes

Munich 1,229,026 Yes Yes No No Yes Yes Yes No Yes

Cologne 953,551 Yes No No No Yes Yes Yes No Yes

Frankfurt 644,865 Yes No No No Yes Yes Yes No Yes

.

.Erlangen

.

.102,440

.

.No

.

.No

.

.No

.

.No

.

.No

.

.Yes

.

.No

.

.No

.

.Yes

0.87 0.77 0.51 0.56 0.75 0.78 0.91 1.00 0.71Cue validities:

Does this cue discriminate?

Consider the most valid unexamined cue

Y

N

Are there any other cues?

NY

A: Choose object with

positive cue value

A: Guess

Which city has a greater population, Berlin or Cologne?

Y

An example: take-the-best

Q:

Objects

Cues

The performance of take-the-best

City Population Soccer?

State capital?

Former GDR?

Industrial belt?

License letter?

Intercity train-line?

Expo site?

National capital?

University?

Berlin 3,433,695 No Yes No No Yes Yes Yes Yes Yes

Hamburg 1,652,363 Yes Yes No No No Yes Yes No Yes

Munich 1,229,026 Yes Yes No No Yes Yes Yes No Yes

Cologne 953,551 Yes No No No Yes Yes Yes No Yes

Frankfurt 644,865 Yes No No No Yes Yes Yes No Yes

.

.Erlangen

.

.102,440

.

.No

.

.No

.

.No

.

.No

.

.No

.

.Yes

.

.No

.

.No

.

.Yes

Sample A

Sample B

Train models

Predictions

Take-the-best:• Fits the data poorly.• Predicts exceptionally well.• The uncertainty of samples

– Regularity vs. randomness.

Heuristics and robustness

Atmospheric disturbances

Aircraft functioning

Changes in samples

Generalization error

Changes to operating conditions

The robustness of heuristics:• A sample of observations only provides an uncertain indicator of

latent environmental regularities.• Ignoring information is one way of increasing robustness.

Robust systems maintain their function despite changes in operating conditions.

No system is robust under all conditions

TTB dominates(white)

TTB inferior(black)

Proportion of the learning curve

dominated by TTB

Low redundancy High redundancy

Environmental operating conditions

Low predictability

High predictability

The big picture: Dealing with uncertainty

Large worlds – “The real world.”• Probabilities/options/actions not

known with certainty.• Robustness becomes more important.• The accuracy-effort trade-off no longer

holds.

Small worlds – “Laboratory conditions.”• Maximize expected utility.• Bayesian updating of probability

distributions.• Need to know the relevant

probabilities/options/actions.

“Small worlds” versus “Large worlds” (Savage, 1954)

Optimization

Satisficing(Simon, 1990)

Summary: Heuristics and uncertainty

An introduction to the study of heuristics:

• Why do organisms rely on heuristics in an uncertain world?

• Heuristics are not poor substitutes for more sophisticated, resource intensive mechanisms.

• Ignoring information and performing less processing can lead to greater accuracy and increased robustness.

• Many examples of less-is-more…

Gigerenzer, G. & Brighton, H. (2009). Homo Heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1, 107-143.