Mimicking the case of rigid robot arms, the set-point regulation problem for ManipUlators with flexible links moving under gravity can be solved by either model-bawd compensation or PID control. The former cannot be applied if an unknown payload is present or when model parameters are poorly estimated, while the latter requires fine and lengthy tuning of gains in order to achieve good performance on the whole workspace. Moreover, no global convergence proof has been yet given for PID control of flexible robot arms. In this paper, a simple iterative scheme is proposed for generating exact gravity compensation at the desired set-point, without the knowledge of rigid or flexible dynamic model terms. The control law starts with a PD action on the error at the joint level, updating at discrete instants an additional feedforward term. Global convergence of the scheme is proved under a mild condition on the proportional gain and a structural property on the arm stiffness, which is usually satisfied in practice. The proposed learning scheme is also extended to the direct control of the end-effector (tip) position. Experimental results are presented for a two-link robot with a flexible forearm moving on a tilted plane.