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Two classes of algorithms for optimization in the presence of noise arepresented, that do not require the evaluation of the objective function. Thefirst generalizes the well-known Adagrad method. Its complexity is thenanalyzed as a function of its parameters. A second class of algorithms is thenderived whose complexity is at least as good as that of the first class.Initial numerical experiments on finite-sum problems arising from deep-learningapplications suggest that methods of the second class may outperform those ofthe first.

Complexity and performance for two classes of noise-tolerant first-order algorithms