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In this paper, we consider both first- and second-order techniques to addresscontinuous optimization problems arising in machine learning. In thefirst-order case, we propose a framework of transition from deterministic orsemi-deterministic to stochastic quadratic regularization methods. We leveragethe two-phase nature of stochastic optimization to propose a novel first-orderalgorithm with adaptive sampling and adaptive step size. In the second-ordercase, we propose a novel stochastic damped L-BFGS method that improves onprevious algorithms in the highly nonconvex context of deep learning. Bothalgorithms are evaluated on well-known deep learning datasets and exhibitpromising performance.

Adaptive First- and Second-Order Algorithms for Large-Scale Machine Learning