English
Related papers

Related papers: High-accuracy log-concave sampling with stochastic…

200 papers

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…

Optimization and Control · Mathematics 2025-11-25 Katya Scheinberg , Miaolan Xie

In this work, we study the convergence \emph{in high probability} of clipped gradient methods when the noise distribution has heavy tails, ie., with bounded $p$th moments, for some $1<p\le2$. Prior works in this setting follow the same…

Optimization and Control · Mathematics 2023-04-05 Ta Duy Nguyen , Alina Ene , Huy L. Nguyen

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

Optimization and Control · Mathematics 2020-02-28 Derek Driggs , Jingwei Liang , Carola-Bibiane Schönlieb

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

Optimization and Control · Mathematics 2019-02-06 Yi Xu , Zhuoning Yuan , Sen Yang , Rong Jin , Tianbao Yang

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen

A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the…

Optimization and Control · Mathematics 2021-01-15 Sébastien Bubeck , Qijia Jiang , Yin Tat Lee , Yuanzhi Li , Aaron Sidford

The study of adaptive data analysis examines how many statistical queries can be answered accurately using a fixed dataset while avoiding false discoveries (statistically inaccurate answers). In this paper, we tackle a question that…

Machine Learning · Computer Science 2023-02-09 Roi Livni

Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the…

Optimization and Control · Mathematics 2025-05-30 Zijian Liu , Zhengyuan Zhou

We consider sum-type strongly convex optimization problem (first term) with smooth convex not proximal friendly composite (second term). We show that the complexity of this problem can be split into optimal number of incremental oracle…

Optimization and Control · Mathematics 2020-03-12 Darina Dvinskikh , Sergey Omelchenko , Alexander Tyurin , Alexander Gasnikov

For deterministic optimization, line-search methods augment algorithms by providing stability and improved efficiency. We adapt a classical backtracking Armijo line-search to the stochastic optimization setting. While traditional…

Optimization and Control · Mathematics 2018-07-24 Courtney Paquette , Katya Scheinberg

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an…

Machine Learning · Computer Science 2021-02-24 Difan Zou , Pan Xu , Quanquan Gu

This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits…

Optimization and Control · Mathematics 2024-04-01 Yu-Hong Dai , Jiani Wang , Liwei Zhang

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately…

Machine Learning · Statistics 2022-04-06 Zhongruo Wang , Krishnakumar Balasubramanian , Shiqian Ma , Meisam Razaviyayn

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with…

Machine Learning · Computer Science 2023-06-08 Blake Woodworth , Konstantin Mishchenko , Francis Bach

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

Optimization and Control · Mathematics 2022-10-06 Melinda Hagedorn , Florian Jarre

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

Machine Learning · Computer Science 2022-02-28 Che-Ping Tsai , Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating…

Optimization and Control · Mathematics 2026-04-20 Shunzhi Zhang , Shichen Liao , Congying Han , Tiande Guo

In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically…

Optimization and Control · Mathematics 2026-02-12 Chuan He , Zhaosong Lu , Defeng Sun , Zhanwang Deng

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Machine Learning · Statistics 2025-05-20 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo