Decision making has been studied with a wide array of tasks. Here we examine the theoretical structure of bandit, information sampling and foraging tasks. These tasks move beyond tasks where the choice in the current trial does not affect future expected rewards. We have modeled these tasks using Markov decision processes (MDPs). MDPs provide a general framework for modeling tasks in which decisions affect the information on which future choices will be made. Under the assumption that agents are maximizing expected rewards, MDPs provide normative solutions. We find that all three classes of tasks pose choices among actions which trade-off immediate and future expected rewards. The tasks drive these trade-offs in unique ways, however. For bandit and information sampling tasks, increasing uncertainty or the time horizon shifts value to actions that pay-off in the future. Correspondingly, decreasing uncertainty increases the relative value of actions that pay-off immediately. For foraging tasks the time-horizon plays the dominant role, as choices do not affect future uncertainty in these tasks.
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