We introduce the spatially correlated multi-armed bandit as a task coupling function learning with the exploration-exploitation trade-off. Participants interacted with bi-variate reward functions on a two-dimensional grid, with the goal of either gaining the largest average score or finding the largest payoff. By providing an opportunity to learn the underlying reward function through spatial correlations, we model to what extent people form beliefs about unexplored payoffs and how that guides search behavior. Participants adapted to assigned payoff conditions, performed better in smooth than in rough environments, and–surprisingly–sometimes performed equally well in short as in long search horizons. Our modeling results indicate a preference for local search options, which when accounted for, still suggests participants were best-described as forming local inferences about unexplored regions, combined with a search strategy that directly traded off between exploiting high expected rewards and exploring to reduce uncertainty about the spatial structure of rewards.