  A class of multi-level algorithms for unconstrained nonlinear optimization is
presented which does not require the evaluation of the objective function. The
class contains the momentum-less AdaGrad method as a particular (single-level)
instance. The choice of avoiding the evaluation of the objective function is
intended to make the algorithms of the class less sensitive to noise, while the
multi-level feature aims at reducing their computational cost. The evaluation
complexity of these algorithms is analyzed and their behaviour in the presence
of noise is then illustrated in the context of training deep neural networks
for supervised learning applications.
