Perfection and bounded rationality in the study of

Perfection and bounded rationality in the study of cognition Henry Brighton

Observations and motivation 1 Cognition rests on an ability to make accurate inferences from limited observations of an uncertain and potentially changing environment. 2 Humans and other animals are resource bounded, and operate subject to constraints. 3 Yet, humans and other animals are remarkably well adapted to uncertain environments. 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 E. g. , 1. Specify the problem the agent is attempting to solve. Inductive inference 2. Develop a model of the environment. Probabilistic model 3. Make minimal assumptions about computational limitations. 4. Derive the optimal response function given 1 -3. Bayesian statistics Successful rational analysis: 5. Does the agent being modeled behave accordingly? Y Ideal observer model ≈ Human responses N Anderson, J. R. (1991). Behavioral & Brain Sciences, 267, 471 -517.

Rational models and process models Explaining Behavior Ideal observer model ≈ Human responses Purposive explanation What does the model tell us? Neutral? Constrains? Identifies? Explaining Machinery S’ Space of processes, S 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

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.

Rational models and process models Explaining Behavior Explaining Machinery Ideal observer model ≈ Human responses Purposive explanation What does the model tell us? The mind might “operate via a set of heuristic tricks, rather than explicit probabilistic computations” Mechanistic explanation (p. 290) Chater, N. , Tenenbaum, J. B. , & Yuille, A. (2006). Trends. In Cognitive Sciences, 10, 287 -291.

What is bounded rationality? 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 Bounded rationality is not the study of how people fail to meet normative ideals… Satisficing Models of bounded rationality attempt to answer the question of how people with limited time, knowledge, money, and other scarce resources make decisions. = meeting an aspiration level = not optimizing = seeking “good enough solutions” Simon, H. A. (1989). The scientist as problem solver. In Complex Information Processing

Peahen mate choice ? Heuristic: Examine 3 -4 males, then choose the one with the most eyespots. Petrie, M. , & Halliday, T. (1994). Behavioral Ecology and Sociobiology, 35, 213– 217.

Example: Decision making in ants Candidate nest sites: (a) 1 st visit (b) (c) 2 nd visit … Lay a pheromone trail Nests half the size yielded reencounter frequencies 1. 96 times greater. Estimate re-encounter freq. 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 Adaptive behavior Simon’s Scissors Metaphor: The organism’s limitations The structure of the environment Simon, H. A. (1956). Psychological Review, 63, 129 -138. 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

General Picture Rational Analysis Explaining Behavior Ideal observer model ≈ Human responses Good-enough observers vs. Ideal observers What does the model tell us? Neutral? Constrains? Identifies? Explaining Machinery S’ Space of processes, S Process level hypothesis Bounded Rationality

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