Robust decision making in uncertain environments Henry Brighton
Feb 21, 2016
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.