arXiv:2607. 07204v1 Announce Type: cross Abstract: Optimization geometrodynamics views optimizer state as evolving geometry.
By Zavier Li
arXiv:2607. 07206v1 Announce Type: new Abstract: Adaptive optimizers mix several mechanisms: a metric or preconditioner maps gradients to descent directions, while estimation, memory, step-size control, constraints, stochasticity, target modification, and discretization determine which directions are available and how they are used.
By Zavier Li
arXiv:2607. 06723v1 Announce Type: cross Abstract: Most gradient-based optimization methods move parameters through a fixed background geometry, even when their internal states implicitly define changing notions of length, curvature, and preconditioning.
By Zavier Li
arXiv:2607. 06723v2 Announce Type: replace-cross Abstract: Adaptive optimizers carry hidden states that change how visible gradients become parameter motion.
By Zavier Li
arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.
By George A Kevrekidis
arXiv:2607. 10808v1 Announce Type: new Abstract: The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed.
By Haricharan Balasundaram, Karthick Krishna Mahendran, Rahul Vaze