Robust decision making in uncertain environments

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Robust decision making in uncertain environments

• Henry Brighton

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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.

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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
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Gaze heuristic
Fix your gaze on the ball, start running, and
adjust your running speed so that the angle of
gaze remains constant.
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Gaze heuristic
Fix your gaze on the ball, start running, and
adjust your running speed so that the angle of
gaze remains constant.
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Gaze heuristic
Fix your gaze on the ball, start running, and
adjust your running speed so that the angle of
gaze remains constant.
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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 dragon?ies 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.

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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.

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Why use heuristics?
The accuracy-effort trade-off
Cost
Accuracy
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.

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The study of heuristics

• Three widely held assumptions
• 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.
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An example take-the-best
Cues
Objects
Cue validities
Does this cue discriminate?
Consider the most valid unexamined cue
A Choose object with positive cue value
Which city has a greater population, Berlin or
Cologne?
Q
Y
N
Are there any other cues?
N
A Guess
Y
Y
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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
Train models
Sample A
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Heuristics and robustness
Robust systems maintain their function despite
changes in operating conditions.
Aircraft functioning
Generalization error
Changes to operating conditions
Atmospheric disturbances
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.

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No system is robust under all conditions
Environmental operating conditions
High predictability
TTB dominates (white)
Proportion of the learning curve dominated by TTB
TTB inferior (black)
Low predictability
Low redundancy
High redundancy
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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/ac
  tions.

Optimization

• Large worlds The real world.
• Probabilities/options/actions not known with
  certainty.
• Robustness becomes more important.
• The accuracy-effort trade-off no longer holds.

Satisficing (Simon, 1990)
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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.