Homo heuristicus: Robust decision making in uncertain environments Henry Brighton

Observations and motivation 3. Yet, humans and other animals are remarkably well adapted to uncertain environments. vision, language, memory, learning, decision making, … 1. Cognition rests on an ability to make accurate inferences from limited observations of an uncertain and potentially changing environment. 2. Computationally, these problems are extremely demanding: “Every problem we look at in AI is NP-complete” (Reddy, 1998). Simple heuristics as robust responses to environmental uncertainty…

Peahen mate choice (Petrie & Halliday, 1994) ? Examine 3-4 males, then choose the one with the most eyespots. Heuristic:

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.

Properties of heuristics Heuristics: Ignore information. Are computationally efficient. –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. α Examine 3-4 males, then choose the one with most eyespots.

Why might an organism rely on a heuristic?

The effort-accuracy trade-off CostAccuracy 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. Worth the extra effort?

Three common assumptions 1.Heuristics provide second-best solutions to problems. 2.We use heuristics because of our cognitive limitations. 3.More information, more computation, and more time would always be better. More information or computation can decrease accuracy… Minds rely on simple heuristics in order to be more accurate… Heuristics as functional responses to environmental uncertainty.

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 Environment E, governed by systematic regularities Sample S of observation s Uncertainty Certainty Hypothesis h 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 OverfittingUnderfitting A good fit is a poor indication of a good model. The model could just be absorbing nonsystematic variation. Ability to predict is a better indicator. Predictive models must capture 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 Examine and explain relative performance Robust design

Take-the-best CityPopulationSoccer team? State capital? Former GDR? Industrial belt? License letter? Intercity train-line? Expo site? National capital? University? Berlin3,433, Hamburg1,652, Munich1,229, Cologne953, Frankfurt644, … Erlangen … 102, Does this cue discriminate? Consider the most valid unexamined cue Y N Are there any other cues? NY Choose object with positive cue value Gues s Which city has a greater population? Cue validities: BerlinCologne FrankfurtMunich

Points of comparison Linear perceptron Feed-forward neural networks Trained using backpropagation Logistic regression as a special case Decision tree inducers Induce a set of rules Uses information theoretic criteria to build tree National capital? Decide Expo site? Soccer team? Decide Intercity train-line? Decide... License plate? Decide... Exemplar methods ? Nearest neighbor classifier CART Stores observations Retrieves similar solutions to solve new problem.

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

CityPopulationSoccer team? State capital? Former GDR? Industrial belt? License letter? Intercity train-line? Expo site? National capital? University? Berlin3,433, Hamburg1,652, Munich1,229, Cologne953, Frankfurt644, … Erlangen … 102, TrainTest Cross-validation Hypothesis h Decisions / Actions

Performance in 20 environments TTB dominates (white) TTB inferior (black) Proportion of the learning curve dominated by TTB Low redundancyHigh redundancy Environmental operating conditions Low predictability High predictability

Why do heuristics work?

The bias-variance dilemma prediction error = (bias) 2 + variance + noise Models suffering from variance Models suffering from bias Dilemma: competing goals, low bias or variance?

Bias and variance prediction error = (bias) 2 + variance + noise variance bias bias usually reflects an inability to model the underlying function variance reflects an oversensitivity to the contents of samples. The short story: Take-the-best outperforms alternative methods by incurring lower variance. It achieves this by ignoring conditional dependencies between cues.

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 Pathogens Immune system Atmospheric conditions Aircraft functioning Robust systems maintain their functioning despite changes in operating conditions.

Variance, robustness, and heuristics The robustness of heuristics: 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. Sample space Hypothesis space U r ≥1 Z r → H Environment E Governed by systematic regularities ∂z∂z ∂h∂h Sampling z1z1 z2z2 h1h1 h2h2 Variance

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 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,