Homo heuristicus: Robust decision making in uncertain environments Henry Brighton

Homo heuristicus:Robust decision making in

uncertain environments

Henry Brighton

Observations and motivation

3. Yet, humans and other animals are remarkably well adapted to uncertain environments.

vision, language, memory, learning, decision making, …

1. Cognition rests on an ability to make accurate inferences from limited observations of an uncertain and potentially changing environment.

2. Computationally, these problems are extremely demanding:

“Every problem we look at in AI is NP-complete”(Reddy, 1998).

Simple heuristics as robust responses to environmental uncertainty…

Peahen mate choice (Petrie & Halliday, 1994)

?

Examine 3-4 males, then choose the one with the most eyespots.

Heuristic:

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 heuristic

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

α

α

Gaze heuristic

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

α

Gaze heuristic

Fix 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 Frisbees (Shaffer et al., 2004).

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

Gaze heuristic

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

Properties of heuristics

Heuristics:

• Ignore information.

• Are computationally efficient.– Do not implement the process of maximization or optimization.

• Satisfice, seek “good enough solutions” (Simon, 1956).

• Are adapted to some environmental contexts at the expense of others.

α

Examine 3-4 males, then choose the one with most eyespots.

Why might an organism rely on a heuristic?

The effort-accuracy trade-off

CostAccuracy

Effort

• Information search and computation cost time and effort.

• Therefore, minds might rely on simple heuristics that are less accurate than strategies that use more information and computation.

Worth the extra effort?

Three common assumptions

1. Heuristics provide second-best solutions to problems.

2. We use heuristics because of our cognitive limitations.

3. More information, more computation, and more time would always be better.

More information or computation can decrease accuracy…

Minds rely on simple heuristics in order to be more accurate…

Heuristics as functional responses to environmental uncertainty.

Overview: Less-is-more

• The problem of inductive inference

• Performance and inductive inference

• Example models of inductive inference

• Examine and explain relative performance

• Robust design

Inductive inference

Environment E, governed by

systematic regularities

Sample S of

observations

Uncertainty

Certainty Hypothesish

Induced hypothesis h:

• Represents a generalization of the observations.

• Allows the organism to second-guess future / unobserved events.

• Used to decide and act…

Decisions /

Actions

Performance

OverfittingUnderfitting

A good fit is a poor indication of a good model. The model could just be absorbing nonsystematic variation.

Ability to predict is a better indicator. Predictive models must capture systematic regularities.

Less-is-more

• The problem of inductive inference– Second-guessing systematic regularities in observations

• Performance and inductive inference– Predictive accuracy, over- and underfitting

• Example models of inductive inference

• Examine and explain relative performance

• Robust design

Take-the-best

City Population Soccer team?

State capital?

Former GDR?

Industrial belt?

License letter?

Intercity train-line?

Expo site?

National capital?

University?

Berlin 3,433,695 0 1 0 0 1 1 1 1 1

Hamburg 1,652,363 1 1 0 0 0 1 1 0 1

Munich 1,229,026 1 1 0 0 1 1 1 0 1

Cologne 953,551 1 0 0 0 1 1 1 0 1

Frankfurt 644,865 1 0 0 0 1 1 1 0 1

…

Erlangen

…

102,440 0 0 0 0 0 1 0 0 1

0.87 0.77 0.51 0.56 0.75 0.78 0.91 1.00 0.71

Does this cue discriminate?

Consider the most valid unexamined

cue

Y

N

Are there any other cues?

NY

Choose object with

positive cue value

Guess

Which city has a greater population?

Cue validities:

Berlin Cologne

Frankfurt Munich

Points of comparison

Linear perceptron

Feed-forward neural networks

• Trained using backpropagation • Logistic regression as a

special case

Decision tree inducers

• Induce a set of rules • Uses information theoretic

criteria to build tree

Nationalcapital?

DecideExposite?

Soccerteam?

Decide

Intercitytrain-line?

Decide . . .Licenseplate?

Decide . . .

Exemplar methods

?

Nearest neighbor classifier

CART

• Stores observations • Retrieves similar solutions

to solve new problem.

Less-is-more

• The problem of inductive inference– Second-guessing systematic regularities in observations

• Performance and inductive inference– Predictive accuracy, over- and underfitting

• Example models of inductive inference– Take-the-best

• Examine and explain relative performance

• Robust design

City Population Soccer team?

State capital?

Former GDR?

Industrial belt?

License letter?

Intercity train-line?

Expo site?

National capital?

University?

Berlin 3,433,695 0 1 0 0 1 1 1 1 1

Hamburg 1,652,363 1 1 0 0 0 1 1 0 1

Munich 1,229,026 1 1 0 0 1 1 1 0 1

Cologne 953,551 1 0 0 0 1 1 1 0 1

Frankfurt 644,865 1 0 0 0 1 1 1 0 1

…

Erlangen

…

102,440 0 0 0 0 0 1 0 0 1

Train Test

Cross-validation

Hypothesish

Decisions / Actions

Performance in 20 environments

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

Why do heuristics work?

The bias-variance dilemmaprediction error = (bias)2 + variance + noise

Models suffering from variance

Models suffering from bias

Dilemma: competing goals, low bias or variance?

Bias and variance

prediction error = (bias)2 + variance + noise

variance

bias

bias usually reflects an inability to model the underlying function

variance reflects an oversensitivity to the contents of samples.The short story:

Take-the-best outperforms alternative methods by incurring lower variance.

It achieves this by ignoring conditional dependencies between cues.

Less-is-more

• The problem of inductive inference– Second-guessing systematic regularities in observations

• Performance and inductive inference– Predictive accuracy, over- and underfitting

• Example models of inductive inference– Take-the-best

• Examine and explain relative performance– Less-is-more via variance reduction

• Robust design

Robustness

Pathogens

Immune system

Atmospheric conditions

Aircraft functioning

Robust systems maintain their functioning despite changes in operating conditions.

Variance, robustness, and heuristics

The robustness of heuristics:

• A sample of observations only provides an uncertain indicator of latent environmental regularities.

• Which design features limit responses to changes in samples?

• Ignoring information is one way of increasing robustness.

Samplespace

Hypothesisspace

Ur ≥1 Zr → H

Environment E

Governed by systematic regularities

∂z

∂h

Sampling

z1 z2

h1

h2

Variance

Less-is-more

• The problem of inductive inference– Second-guessing systematic regularities in observations

• Performance and inductive inference– Predictive accuracy, over- and underfitting

• Example models of inductive inference– Take-the-best

• Examine and explain relative performance– Less-is-more via variance reduction

• Robust design– Ignoring information can limit sensitivity to perturbations

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.