Bounded Perception and Learning how to Decide

Karl Schlag

No 972, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: Consider a decision maker who must coordinate his decision with the occurrence of some phenomenon. In order to behave "optimally," the circumstances surrounding the occurrence of the phenomenon must be learned. However, there are natural bounds on the capabilities of perception. More specifically, only a fixed number of attributes may be focused on and observed in each instance. This paper models this problem in the framework of learning concepts from positive examples involving bounded perception. For clarity and simplicity, it is assumed that for each positive example the decision maker may only observe on of its attributes. The analysis concentrates on finding optimal ways of specifying what attributes should be observed. With certain assumptions of independence we show that a class of local "hillclimbing" algorithms are essentially the only optimal ones. Additionally it is shown that patterns in the observation behavior emergence asymptotically. The results underscore the importance of diversifying attention when acquiring knowledge.

Date: 1991-12
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