Optimal allocation of attention in a signal detection task

Abstract

Detection of temporally uncertain signals is a common motif in many real world and laboratory settings including tasks that require sustained attention. While the role of attention in these tasks has been studied extensively, there have not been many normative accounts of attentional allocation in such tasks. In this study, we investigated optimal behavior in a signal detection task with uncertain signal onset where we allowed attention to improve the quality of sensory information collected. However, paying attention came at a cost and so, attention had to be allocated wisely. Using dynamic programming, we estimated an optimal policy for allocating attention within each trial of the task. Interestingly, we found that a rational agent must pay attention only when there is enough (but not overwhelming) evidence in favor of a signal. Further, for the same amount of evidence, it was optimal to pay more attention later in the trial. Reward-cost trade-offs dictated that when a trial was too tough or when there was too much bias towards a certain hypothesis, there is no advantage in paying attention. The performance (as measured by the sensitivity index, d') was a result of complex interactions between factors like signal length, signal probability and attention costs. It increased with signal length, decreased with attention costs only at short signal lengths and remained unchanged with signal probability (despite a shift in the response criterion). Equivalent results have been shown experimentally in sustained attention tasks which are known to involve a similar temporal uncertainty.