Transcript Document

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 heuristic
Fix your gaze on the ball, start running,
and adjust your running speed so that the
angle of gaze remains constant.
Gaze heuristic
Fix your gaze on the ball, start running,
and adjust your running speed so that the
angle of gaze remains constant.
Gaze heuristic
Fix your gaze on the ball, start running,
and adjust your running speed so that the
angle of gaze remains constant.
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 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?
The accuracy-effort trade-off
Accuracy
Cost
Effort
•
•
•
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
Three widely held assumptions:
1.
2.
3.
Heuristics are always second-best.
We use heuristics only because of our cognitive limitations.
More information, more computation, and more time would always be
better.
A stronger hypothesis, the possibility that less-is-more:
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.
An example: take-the-best
Cues
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
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
0.71
Cologne
Cue validities:
Q: Which city has a greater
population, Berlin or
Cologne?
Consider the most
valid unexamined cue
Does this cue
discriminate?
Y
A:
Choose
object
with
positive
cue value
N
Y
Are there any
other cues?
N
Y
A: Guess
Objects
The performance of take-the-best
Take-the-best:
•
Fits the data poorly.
•
Predicts exceptionally well.
•
The uncertainty of samples
–
Regularity vs. randomness.
Predictions
Sample B
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
Train models
Sample A
Heuristics and robustness
Robust systems maintain their function despite changes in operating conditions.
Aircraft functioning
Atmospheric disturbances
Generalization error
Changes to
operating
conditions
Changes in samples
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.
No system is robust under all conditions
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
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.