arXiv:2607. 03519v1 Announce Type: new Abstract: We show that projected Adam for online optimization with arbitrary moment decay parameters $\beta_1,\beta_2\in[0,1)$ can have average regret bounded away from zero.
arXiv:2602.08372v2 Announce Type: replace Abstract: We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL...
arXiv:2607. 27383v1 Announce Type: new Abstract: We establish the first convergence guarantees for the plain vector-form \emph{Adam} optimizer under heavy-tailed stochastic noise.
The paper establishes uniform a priori bounds for the Adam optimizer, enabling an unconditional error analysis for a broad class of strongly convex stochastic optimization problems. Prior analyses were conditional, assuming Adam remained bounded, whereas this work removes that assumption. The results provide a rigorous foundation for Adam’s performance in training deep neural networks and other convex optimization tasks.
arXiv:2608. 15824v1 Announce Type: new Abstract: Adam retains a moving average of past squared gradients in its denominator, but the optimization cost of this memory is not well understood.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2601.13519v4 Announce Type: replace-cross Abstract: This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the...
arXiv:2510. 22819v3 Announce Type: replace Abstract: The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time.
arXiv:2608.30382v1 Announce Type: new Abstract: Popular adaptive stochastic gradient descent (SGD) methods to train artificial intelligence (AI) systems include the RMSprop, the Adam, and the AdamW o...
arXiv:2609.37787v1 Announce Type: new Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
The paper investigates how Adam’s update rule relates to natural gradient descent (NGD) by treating Adam as a diagonal empirical Fisher approximation with additional factors such as diagonal truncation, empirical label substitution, and temporal lag. Using a scale‑invariant metric, the authors quantify Adam’s geometric deviation from true NGD across four loss landscapes—well‑conditioned and ill‑conditioned linear regression, logistic regression, and a small neural network—finding that deviation is low in well‑conditioned settings but can reach about 10³ in ill‑conditioned or non‑convex scenarios. Despite higher geometric drift correlating with slower early optimization, Adam still achieves low final loss, and the improved empirical Fisher (iEF) yields more stable trajectories than the standard empirical Fisher (EF).
arXiv:2608. 20638v1 Announce Type: cross Abstract: The edge-of-stability (EoS) phenomenon of Adam has been widely observed, while its underlying dynamical mechanism is not yet fully understood.
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.