Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information
This addresses optimization challenges in machine learning by providing a versatile algorithm with convergence guarantees, though it appears incremental as an adaptive method building on existing second-order approaches.
The paper tackles the problem of adaptive optimization in large-scale machine learning by introducing a method that dynamically adjusts search direction and step-size using local curvature and Lipschitz smoothness estimates, eliminating the need for manual learning rate tuning. It demonstrates strong performance compared to state-of-the-art methods through empirical evaluation on standard problems.
We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.