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We present a novel adaptive optimization algorithm for large-scale machinelearning problems. Equipped with a low-cost estimate of local curvature andLipschitz smoothness, our method dynamically adapts the search direction andstep-size. The search direction contains gradient information preconditioned bya well-scaled diagonal preconditioning matrix that captures the local curvatureinformation. Our methodology does not require the tedious task of learning ratetuning, as the learning rate is updated automatically without adding an extrahyperparameter. We provide convergence guarantees on a comprehensive collectionof optimization problems, including convex, strongly convex, and nonconvexproblems, in both deterministic and stochastic regimes. We also conduct anextensive empirical evaluation on standard machine learning problems,justifying our algorithm's versatility and demonstrating its strong performancecompared to other start-of-the-art first-order and second-order methods.

Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information