The capability of directing gaze to relevant parts in the environment is crucial for our survival. Computational models have proposed quantitative accounts of human gaze selection in a range of visual search tasks. Initially, models suggested that gaze is directed to the locations in a visual scene at which some criterion such as the probability of target location, the reduction of uncertainty or the maximization of reward appear to be maximal. But subsequent studies established, that in some tasks humans instead direct their gaze to locations, such that after the single next look the criterion is expected to become maximal. However, in tasks going beyond a single action, the entire action sequence may determine future rewards thereby necessitating planning beyond a single next gaze shift. While previous empirical studies have suggested that human gaze sequences are planned, quantitative evidence for whether the human visual system is capable of fnding optimal eye movement sequences according to probabilistic planning is missing. Here we employ a series of computational models to investigate whether humans are capable of looking ahead more than the next single eye movement. We found clear evidence that subjects’ behavior was better explained by the model of a planning observer compared to a myopic, greedy observer, which selects only a single saccade at a time. In particular, the location of our subjects’ frst fxation difered depending on the stimulus and the time available for the search, which was well predicted quantitatively by a probabilistic planning model. Overall, our results are the frst evidence that the human visual system’s gaze selection agrees with optimal planning under uncertainty

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