Abstract: Embodiments disclose a system for determining a sensitivity of a networked system. The system identifies a vertex (V) that represents a constituent and a state of the constituent, and an interaction (E) between at least two Vs. An interaction-dependent function provides a probability that, when a perturbation occurs, a V will be in a certain state given that it is currently in a determined state and its neighbors are currently in determined states. A network reliability is used to determine a probability that a V's state holds when a perturbation occurs. The system evaluates only a certain amount of terms in a Taylor series from a sample, and identifies interpolating polynomials between the Taylor series. A cost function optimizes a property of the networked system for a fixed cost. The system perturbs the networked system until reliability is zero to estimate a sensitivity of the networked system.