This paper introduces a new global optimization algorithm that solves the threshold estimation problem.In this active learning problem, underlying many empirical neuroscience and psychophysics experiments, the objective is to estimate the input values that would produce the desired output value from an unknown, noisy, non-decreasing response function. Compared to previous approaches, ZOOM (Zooming Optimistic Optimization Method) offers the best of both worlds: ZOOM is model-agnostic, benefits from stronger theoretical guarantees and faster convergence rate, but also quickly jumps between arms, offering strong performance even for small sampling budgets.