Perfection and bounded rationality in the study of cognition

Henry Brighton

Observations and motivation

Yet, humans and other animals are remarkably well adapted to uncertain environments.

Cognition rests on an ability to make accurate inferences from limited observations of an uncertain and potentially changing environment.

Humans and other animals are resource bounded, and operate subject to constraints.

1

2 3

Understanding how organisms solve inference problems can inform the understanding of

learning machinery more generally.

Workshop questions

A. How can we formalize rational decision making for “imperfect decision makers”?

B. How can we create a prescriptive theory which takes into account imperfect decision makers?

C. How can we extend/modify existing theories to account for imperfect decision makers?

Assumption:

Constraints, limitations, resource bounds, etc. are imperfections?

The rational analysis of cognition

1. Specify the problem the agent is attempting to solve.

2. Develop a model of the environment.

3. Make minimal assumptions about computational limitations.

4. Derive the optimal response function given 1-3.

5. Does the agent being modeled behave accordingly?

Anderson, J. R. (1991). Behavioral & Brain Sciences, 267, 471-517.

Inductive inference

Probabilistic model

Bayesian statistics

Ideal observer

model

Human responses≈

Y

N

Successful rational analysis:

E.g.,

Rational models and process models

ExplainingBehavior

ExplainingMachinery

Ideal observer

model

Human responses≈

Space of processes, S

S’

Constrains?

Neutral?

Identifies?

What does the model tell us?Purposive explanation

Mechanistic explanation

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.

Rational models and process models

ExplainingBehavior

ExplainingMachinery

Ideal observer

model

Human responses≈

What does the model tell us?Purposive explanation

Mechanistic explanationThe mind might “operate via a set of heuristic tricks, rather than explicit probabilistic computations” (p. 290)

Chater, N., Tenenbaum, J. B., & Yuille, A. (2006). Trends. In Cognitive Sciences, 10, 287-291.

What is bounded rationality?

Models of bounded rationality attempt to answer the question of how people with limited time, knowledge, money, and other scarce resources make decisions.

Bounded rationality is not the study of how people fail to meet normative ideals…

Herbert Simon’s question:

“How do human beings reason when the conditions for

rationality postulated by the model of neoclassical

economics are not met?”

Which is knowledge of:

• All the relevant alternatives

• Their consequences

• Their probabilities

• A predictable world without surprises

= not optimizing

= meeting an aspiration level

Satisficing

= seeking “good enough solutions”

Simon, H. A. (1989). The scientist as problem solver. In Complex Information Processing

Peahen mate choice

?

Examine 3-4 males, then choose the one with the most eyespots.

Heuristic:

Petrie, M., & Halliday, T. (1994). Behavioral Ecology and Sociobiology, 35, 213–217.

Candidate nest sites:

1st visit 2nd visit

Lay a pheromone trail Estimate re-encounter freq.

Nests half the size yielded reencounter

frequencies 1.96 times greater.

Example: Decision making in ants

(a) (b) (c)

Ants perfect decision makers?

• Is 1.96 optimal, or just good enough?

• Are 2-3 visits optimal, or just good enough?

• Group level aggregation

…

Mugford, S. T., Mallon, E. B., & Franks, N. R. (2001). Behavioral Ecology, 12, 655–658.

The study of simple heuristics

Can ignoring information improve performance?

For example:

• Ignoring cues

• Ignoring dependencies between cues

• Restricting cue weights

Imposing “imperfections” onto existing learning algorithms

Gigerenzer, G. & Brighton, H. (2009). Topics in Cognitive Science, 1, 107-143

Simon’s Scissors Metaphor:

The organism’s limitations

The structure of the environment

Adaptive behavior

Simon, H. A. (1956). Psychological Review, 63, 129-138.

General Picture

ExplainingBehavior

ExplainingMachinery

Ideal observer

model

Human responses≈

Space of processes, S

S’

Constrains?

Neutral?

Identifies?

What does the model tell us?

Rational Analysis

Bounded Rationality

Process level hypothesis

Good-enough observers vs.Ideal observers

Workshop questions

A. How can we formalize “rational decision making” for “imperfect decision makers”?

B. How can we create a prescriptive theory which takes into account imperfect decision makers?

C. How can we extend/modify existing theories to account for imperfect decision makers?

Constraints and limitations:• Should not always be seen as imperfections• Can serve an adaptive benefit• Understanding when and why is the question