arXiv Machine Learning By Binghui Peng

A Resolution of the SS--RS--GD Inequalities

Read the original on arXiv Machine Learning →

arXiv:2607. 22620v1 Announce Type: cross Abstract: Yun, Sra, and Jadbabaie (COLT 2021, open question) conjectured the SS--RS--GD inequalities: for well-conditioned symmetric matrices $A_1,\dots,A_n$, the operators $W_{ss}$, $W_{rs}$, and $W_{gd}$ that encode the expected iterate of single-shuffle SGD, random-reshuffle SGD, and gradient descent on a quadratic finite sum should satisfy \[ \|W_{ss}\|\le \| W_{rs}\|\le \|W_{gd}\|.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
Jul 14

Lower Bound on the Cumulative Constrained Violation for the OGD+Projection algorithm for Constrained Online Convex Optimization (COCO)

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
arXiv Machine Learning
Jun 16

Phase Transition in Convex Relaxations for Graph Alignment

arXiv:2606. 15581v1 Announce Type: cross Abstract: We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+\sigma^2}$.

By Laurent Massouli\'e, Sushil Mahavir Varma, Louis Vassaux, Ir\`ene Waldspurger
arXiv Machine Learning
Aug 10

Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

arXiv:2608. 06687v1 Announce Type: cross Abstract: We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations $\mathfrak L_\beta u=f$ using linearized ReLU$^k$ neural networks on the sphere, where $\mathfrak L_\beta$ is a positive elliptic spectral multiplier of order $\beta$.

By Xinliang Liu, Tong Mao, Jinchao Xu