We consider the reduced Allen–Cahn action functional, which appears as the sharp interface limit of the Allen–Cahn action functional and can be understood as a formal action functional for a stochastically perturbed mean curvature flow. For suitable evolutions of generalized hypersurfaces this functional consists of the sum of the squares of the mean curvature and the velocity vectors, integrated over time and space. For given initial and final conditions we investigate the corresponding action minimization problem.