We study the problem of an optimal oculomotor control during the execution of visual search tasks. We introduce a computational model of human eye movements, which takes into account various constraints of the human visual and oculomotor systems. In the model, the choice of the subsequent fixation location is posed as a problem of a stochastic optimal control, which relies on reinforcement learning methods. We show that if biological constraints are taken into account, the trajectories simulated under a learned policy share both basic statistical properties and a scaling behaviour with human eye movements. We validated our model simulations with human psychophysical eye-tracking experiments.

The problem of gaze allocation has previously been studied in the framework of eye-movement control models, which require prior knowledge of visibility maps (VMs). These encode the signal-to-noise ratio, at each point in the visual field, which can be used to define an optimal policy of gaze allocation. However, it is not always possible to estimate the VM, in a given experimental setting, as it depends on many factors, including the visual system of the individual observer. Hence, few eye-movement datasets include the corresponding VM estimates. This can be problematic for the analysis of certain clinical conditions, such as Age-related Macular Degeneration (AMD), which are associated with reduced sensitivity in the affected locations of the visual field. The corresponding VMs are highly idiosyncratic, and cannot be modeled by estimates obtained from healthy observers. We propose an algorithm for maximum likelihood VM estimation, working directly from eye-movement sequences. We apply this algorithm to two eye-tracking datasets, based on visual search tasks, obtained from AMD patients. We show that the inferred VMs are spatially consistent with the measured visual field sensitivities. We also show that simulations with the estimated VMs can account for the asymmetric distribution of saccade vectors, which is typical of AMD patients.

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