Bilevel optimization (BLO) is fundamental to hierarchical decision-making but suffers from critical instability under heavy-tailed stochastic noise. Existing variance-reduction techniques typically rely on myopic magnitude checks, which fail to distinguish informative geometric signals from impulsive outliers.
arXiv:2505.13299v2 Announce Type: replace-cross
Abstract: This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the...
By Likai Chen, Georg Keilbar, Wei Biao Wu
arXiv:2610.28107v1 Announce Type: cross
Abstract: Gradient clipping is a key tool for obtaining high-probability convergence guarantees for stochastic first-order methods under heavy-tailed noise. Ex...
By Alyona Nekrasova, Makar Sidorov, Savelii Chezhegov, Alexander Gasnikov, Margarita Preobrazhenskaia, Igor Preobrazhensky, Eduard Gorbunov
arXiv:2610.32850v1 Announce Type: cross
Abstract: Estimating the conditional distribution of multivariate responses with continuous and binary components requires capturing their dependence, respecti...
By Seyong Hwang, Kean Ming Tan, Ji Zhu
arXiv:2610. 12865v1 Announce Type: new Abstract: Existing convergence guarantees for non-log-concave sampling with stochastic gradient Langevin Monte Carlo (SG-LMC) typically assume globally Lipschitz gradients and uniformly bounded noise variance.
By M. Berk Sahin, Ege C. Kaya, Arda Fazla, Behzad Sharif, Abolfazl Hashemi
The paper tackles two key gaps in streaming PCA using Oja's algorithm: it establishes sharp operator‑norm convergence for general‑rank subspaces under sub‑Gaussian data, and it provides distributional inference for the resulting subspace estimator. The authors remove non‑vanishing remainder terms from existing analyses, achieving rates that match minimax bounds in both dense‑tail and sparse‑tail regimes. They further develop a linearization of Oja’s iterates, enabling high‑dimensional Gaussian approximations and an online multiplier bootstrap for practical inference.
By Haoshu Xu, Hongzhe Li