Complexities of Armijo-like algorithms in Deep Learning context

Abstract: The classical Armijo backtracking algorithm achieves the optimal complexity for smooth functions like gradient descent but without any hyperparameter tuning. However, the smoothness assumption is not suitable for Deep Learning optimization. In this work, we show that some variants of the Armijo optimizer achieves acceleration and optimal complexities under assumptions more suited for Deep Learning: the (L 0 , L 1 ) smoothness condition and analyticity. New dependences on the smoothness constants and the initial gap are established. The results theoretically highlight the powerful efficiency of Armijo-like conditions for highly non-convex problems.