The paper studies algorithms for computing the Entropic Gromov-Wasserstein (EGW) distance, a measure of discrepancy between metric measure spaces. It introduces Averaged Mirror Descent (AMD), which averages successive Mirror Descent steps and is proven to converge for any cost function, and shows that a dual gradient method with a fixed step size also converges for arbitrary costs, even when iterations are inexact. Empirical comparisons demonstrate that both AMD and the dual gradient method succeed on cases where classical Mirror Descent fails.
By Joanna Marks, Gabriel Rioux, Riccardo Passeggeri
arXiv:2609.06064v1 Announce Type: cross
Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...
By Tianxi Zhu, Yi Xu, Xiangyang Ji
arXiv:2606. 00520v1 Announce Type: cross Abstract: Many stochastic gradient methods are believed not to converge when the noise in stochastic gradients has only a finite $p$-th moment for $p\in\left(1,2\right)$, a setting known as the heavy-tailed noise assumption.
By Zijian Liu
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
By Andrea Montanari, Kangjie Zhou
arXiv:2502. 00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization.
By Dingzhi Yu, Wei Jiang, Hongyi Tao, Yuanyu Wan, Lijun Zhang
The paper introduces a distributionally robust method for learning hyperparameters of first‑order convex optimization algorithms. By minimizing a Wasserstein‑robust performance estimation problem over a dataset of problem instances, the approach interpolates between classical learning‑to‑optimize (L2O) and worst‑case PEP design. The authors solve the resulting problem with stochastic gradient descent, provide high‑probability risk bounds, and demonstrate that the learned algorithms outperform both worst‑case optimal and vanilla L2O baselines on logistic regression, LASSO, and linear programming tasks.
By Vinit Ranjan, Jisun Park, Bartolomeo Stellato