Researchers have developed new deterministic methods inspired by the Adam optimizer, aiming to improve convergence rates for smooth convex objectives. These methods, Adam-HNAG and Adam-HNAG-s, utilize a variable-and-operator splitting technique to decouple momentum and adaptive preconditioning. By incorporating a Hessian-driven correction and Adam-style gradient feedback, the new algorithms demonstrate a discrete Lyapunov contraction, leading to an O(k^-2) objective-value bound under specific conditions. Numerical experiments suggest these methods offer improved performance compared to the original Adam recursion. AI
IMPACT Introduces novel optimization techniques that could enhance the training efficiency of machine learning models.
RANK_REASON Academic paper detailing new optimization algorithms. [lever_c_demoted from research: ic=1 ai=1.0]
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