SUPER-ADAM: Faster and Universal Framework of Adaptive Gradients
This provides a faster and more flexible framework for adaptive gradient methods in machine learning, though it is incremental as it builds on existing techniques.
The authors tackled the lack of a universal adaptive gradient framework with theoretical guarantees for general problems by proposing SUPER-ADAM, which achieves the best known gradient complexity of $ ilde{O}(ε^{-3})$ for nonconvex optimization and outperforms existing adaptive algorithms in deep learning tasks.
Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also only work for specific problems by using some specific adaptive learning rates. Thus, it is desired to design a universal framework for practical algorithms of adaptive gradients with theoretical guarantee to solve general problems. To fill this gap, we propose a faster and universal framework of adaptive gradients (i.e., SUPER-ADAM) by introducing a universal adaptive matrix that includes most existing adaptive gradient forms. Moreover, our framework can flexibly integrate the momentum and variance reduced techniques. In particular, our novel framework provides the convergence analysis support for adaptive gradient methods under the nonconvex setting. In theoretical analysis, we prove that our SUPER-ADAM algorithm can achieve the best known gradient (i.e., stochastic first-order oracle (SFO)) complexity of $\tilde{O}(ε^{-3})$ for finding an $ε$-stationary point of nonconvex optimization, which matches the lower bound for stochastic smooth nonconvex optimization. In numerical experiments, we employ various deep learning tasks to validate that our algorithm consistently outperforms the existing adaptive algorithms. Code is available at https://github.com/LIJUNYI95/SuperAdam