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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.