Can brains perform second-order optimization?

In ecological setup, a wide variety of organisms search over space to obtain reward using information obtained via multiple senses. In the simplest scenario of scalar search, a single quantity, e.g. concentration of a chemoattractant, is measured at different locations. Though gradient is considered a crucial component of scalar search, whether organisms rely solely on the gradient is unknown. We hypothesized that scalar search benefits from information other than gradient, including curvature (second-order derivatives) and long-term memory information integration. To test our hypothesis, we devised an information foraging task. In our task, human subjects control a circular avatar to find a peak of the contour by making brief fixations. They were rewarded when they approached the peak within the predefined maximum number of fixations. In our preliminary data, observed search trajectories deviated from what is expected from the gradient-based search, suggesting that the subjects utilized information beyond the gradient. We also manipulated the perception and action components of the task to examine the sensitivity of the adopted strategies to variations of the task design.