arXiv:2402.04691v5 Announce Type: replace-cross
Abstract: This study investigates the use of stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We study weak and str...
By Lei Shi, Jia-Qi Yang
arXiv:2405. 11667v2 Announce Type: replace Abstract: Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD.
By Kumar Kshitij Patel, Margalit Glasgow, Ali Zindari, Lingxiao Wang, Sebastian U. Stich, Ziheng Cheng, Nirmit Joshi, Nathan Srebro
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
By Feng Zhu, Robert W. Heath Jr., Aritra Mitra
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying
arXiv:2608. 06563v1 Announce Type: new Abstract: Machine learning and optimization have advanced together, with practical demands motivating new theory and theoretical breakthroughs enabling new applications.
By Grigory Malinovsky
arXiv:2603. 16481v3 Announce Type: replace Abstract: Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control.
By Amon Lahr, Anna Scampicchio, Johannes K\"ohler, Melanie N. Zeilinger