Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
Modeling Adagrad, RMSProp, and Adam with Integro- Differential equations
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An input-to-state Lyapunov function is introduced to prove global asymptotic stability of RMSProp for constant step sizes and robustness to arbitrary bounded time-varying step size rules.
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Adam-HNAG: A Convergent Reformulation of Adam with Accelerated Rate
Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
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Global Stability and Step Size Robustness of RMSProp
An input-to-state Lyapunov function is introduced to prove global asymptotic stability of RMSProp for constant step sizes and robustness to arbitrary bounded time-varying step size rules.