Homo heuristicus:
Robust decision making in
uncertain environments
Henry Brighton
Observations and motivation
1. Cognition rests on an ability to make
accurate inferences from limited observations
of an uncertain and potentially changing
environment.
vision, language,
memory, learning,
decision making, …
2. Computationally, these problems
are extremely demanding:
“Every problem we look at in AI is NP-complete”
(Reddy, 1998).
3. Yet, humans and other animals
are remarkably well adapted to
uncertain environments.
Simple heuristics as robust
responses to environmental
uncertainty…
Peahen mate choice (Petrie & Halliday, 1994)
?
Heuristic:
Examine 3-4 males, then choose the one with the most eyespots.
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
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.
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.
Properties of heuristics
Examine 3-4 males,
then choose the one
with most eyespots.
Heuristics:
•
Ignore information.
•
Are computationally efficient.
–
α
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.
Why might an organism
rely on a heuristic?
The effort-accuracy trade-off
Worth the extra effort?
Accuracy
Cost
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.
Three common assumptions
1.
Heuristics provide second-best solutions to problems.
Heuristics as functional responses to environmental uncertainty.
2.
We use heuristics because of our cognitive limitations.
Minds rely on simple heuristics in order to be more accurate…
3.
More information, more computation, and more time
would always be better.
More information or computation can decrease accuracy…
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
Hypothesis
h
Certainty
Environment
E, governed by
systematic
regularities
Sample S
of
observation
s
Uncertainty
Induced hypothesis h:
•
Represents a generalization of the observations.
•
Allows the organism to second-guess future / unobserved events.
•
Used to decide and act…
Decision
s/
Actions
Performance
Ability to predict is a better indicator.
Predictive models must capture
systematic regularities.
Underfitting
Overfitting
A good fit is a poor indication of a
good model. The model could just be
absorbing nonsystematic variation.
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
Cue validities:
Berlin
Cologne
Frankfurt
Munich
Consider the most
valid unexamined
cue
0.91
Does this cue
discriminate?
1.00
Y
0.71
Choose
object
with
positive
cue value
N
Which city has a greater
population?
Y
Are there any
other cues?
N
Gues
s
Points of comparison
Feed-forward neural networks
•
•
Decision tree inducers
Trained using backpropagation
Logistic regression as a
special case
•
•
Induce a set of rules
Uses information theoretic
criteria to build tree
Exemplar methods
National
capital?
Decide
Expo
site?
Linear perceptron
Soccer
team?
...
Stores observations
Retrieves similar solutions
to solve new problem.
Intercity
train-line?
Decide
License
plate?
•
•
...
Decide
?
Decide
CART
Nearest neighbor classifier
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
Cross-validation
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
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
Cologne
Train
Test
Hypothesis
h
Decisions /
Actions
Performance in 20 environments
High predictability
Environmental operating conditions
TTB dominates
(white)
Proportion of the
learning curve
dominated by TTB
TTB inferior
(black)
Low predictability
Low redundancy
High redundancy
Why do heuristics work?
The bias-variance dilemma
prediction error = (bias)2 + variance + noise
Models
suffering
from bias
Models suffering
from variance
Dilemma: competing goals, low bias or variance?
Bias and variance
prediction error = (bias)2 + variance + noise
bias usually reflects an
inability to model the
underlying function
bias
variance
The short story:
Take-the-best outperforms
alternative methods by
incurring lower variance.
It achieves this by ignoring
conditional dependencies
between cues.
variance reflects an
oversensitivity to the
contents of samples.
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
Robust systems maintain their functioning despite changes in operating conditions.
Immune system
Aircraft functioning
Pathogens
Atmospheric conditions
Variance, robustness, and heuristics
Variance
The robustness of heuristics:
Hypothesis
space
h2
h1
•
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.
∂h
Ur ≥1 Zr → H
Sample
space
z1
z2
∂z
Sampling
Environment E
Governed by
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
– 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
“Small worlds” versus “Large worlds” (Savage, 1954)
Small worlds – “Laboratory conditions.”
•
Maximize expected utility.
•
Bayesian updating of probability
distributions.
•
Need to know the relevant
probabilities/options/actions.
Large worlds – “The real world.”
•
Probabilities/options/actions not
known with certainty.
•
Robustness becomes more
important.
•
The accuracy-effort trade-off no
longer holds.
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.