We present an algorithm for learning the boundary between an upward-closed set X and its downward-closed complement. The algorithm selects sampling points for which it submits membership queries x ∈ X. Based on the answers and relying on monotonicity, it constructs an approximation of the boundary. The algorithm generalizes binary search on the continuum from one-dimensional (and linearly-ordered) domains to multi-dimensional (and partially-ordered) ones. Applications include the approximation of Pareto fronts in multi-criteria optimization and parameter synthesis for predicates where the influence of parameters is monotone.