Abstract
What kind of strategies subjects follow in various behavioral circumstances has been a central issue in decision making. In particular, which behavioral strategy, maximizing or matching, is more fundamental to animal's decision behavior has been a matter of debate. Here, we prove that any algorithm to achieve the stationary condition for maximizing the average reward should lead to matching when it ignores the dependence of the expected outcome on subject's past choices. We may term this strategy of partial reward maximization “matching strategy”. Then, this strategy is applied to the case where the subject's decision system updates the information for making a decision. Such information includes subject's past actions or sensory stimuli, and the internal storage of this information is often called “state variables”. We demonstrate that the matching strategy provides an easy way to maximize reward when combined with the exploration of the state variables that correctly represent the crucial information for reward maximization. Our results reveal for the first time how a strategy to achieve matching behavior is beneficial to reward maximization, achieving a novel insight into the relationship between maximizing and matching.
Highlights
How do animals, including humans, determine appropriate behavioral responses when their behavioral outcomes are uncertain? Decision-making is a fundamental process of the brain for organizing behaviors, and depends crucially on how subjects have been rewarded in their past behavioral responses
A well-known example includes the reinforcement learning theory based on the temporal difference (TD) error algorithm[1], which is powerful enough to solve difficult problems in machine control and accounts for the basal-ganglia activity representing reward expectancy in monkeys and humans[2,3,4]
We focus on the matching law
Summary
Decision-making is a fundamental process of the brain for organizing behaviors, and depends crucially on how subjects have been rewarded in their past behavioral responses. A well-known example includes the reinforcement learning theory based on the temporal difference (TD) error algorithm[1], which is powerful enough to solve difficult problems in machine control and accounts for the basal-ganglia activity representing reward expectancy in monkeys and humans[2,3,4]. Many algorithms in machine learning and other brain-style computations aim at reward maximization or, somewhat more generally, optimization of a given cost function. Animals often exhibit matching behavior in a variety of decision-making tasks[6,7,8,9], even if such behavior does not necessarily maximize reward. Matching and maximizing are mathematically equivalent in simple tasks[10,11], but not in arbitrary tasks[12,13,14,15]
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