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Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane

The empirical evidence indicates that stochastic optimization with heavy-tailed gradient noise is more appropriate to characterize the training of machine learning models than that with standard bounded gradient variance noise. Most…

Machine Learning · Computer Science 2026-01-28 Hongxu Chen , Ke Wei , Xiaoming Yuan , Luo Luo

In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients,…

Optimization and Control · Mathematics 2022-02-15 Krishnakumar Balasubramanian , Saeed Ghadimi , Anthony Nguyen

Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond…

Optimization and Control · Mathematics 2021-02-12 Vien V. Mai , Mikael Johansson

This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise,…

Machine Learning · Computer Science 2026-05-26 Zhuanghua Liu , Luo Luo

We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than $\mathcal{O}(K^{-2(\alpha - 1)/\alpha})$, when the…

Optimization and Control · Mathematics 2024-04-18 Nikita Puchkin , Eduard Gorbunov , Nikolay Kutuzov , Alexander Gasnikov

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a…

Optimization and Control · Mathematics 2021-07-20 Kevin Huang , Shuzhong Zhang

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…

Optimization and Control · Mathematics 2020-10-26 Eduard Gorbunov , Marina Danilova , Alexander Gasnikov

This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…

Optimization and Control · Mathematics 2026-04-17 Qi Deng , Guanghui Lan , Zhenwei Lin

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via…

Optimization and Control · Mathematics 2016-05-20 Xiao Wang , Shiqian Ma , Ya-xiang Yuan

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

Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…

Optimization and Control · Mathematics 2023-07-18 Wei Liu , Qihang Lin , Yangyang Xu

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…

We consider the problem of finding stationary points in Bilevel optimization when the lower-level problem is unconstrained and strongly convex. The problem has been extensively studied in recent years; the main technical challenge is to…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Hanbaek Lyu

We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…

Optimization and Control · Mathematics 2023-11-03 Billy Jin , Katya Scheinberg , Miaolan Xie

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…

Optimization and Control · Mathematics 2025-06-26 Zhaosong Lu , Yifeng Xiao

This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…

Optimization and Control · Mathematics 2025-11-18 Cac Phan , Kai Wang

We give nearly matching upper and lower bounds on the oracle complexity of finding $\epsilon$-stationary points ($\| \nabla F(x) \| \leq\epsilon$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local…

Machine Learning · Computer Science 2019-02-15 Dylan J. Foster , Ayush Sekhari , Ohad Shamir , Nathan Srebro , Karthik Sridharan , Blake Woodworth

We study stochastic nonconvex optimization under heavy-tailed noise. In this setting, the stochastic gradients only have bounded $p$-th central moment ($p$-BCM) for some $p \in (1,2]$. Building on the foundational work of Arjevani et al.…

Optimization and Control · Mathematics 2026-04-01 Adrien Fradin , Abdurakhmon Sadiev , Laurent Condat , Peter Richtárik

Stochastic optimization is fundamental to modern machine learning. Recent research has extended the study of stochastic first-order methods (SFOMs) from light-tailed to heavy-tailed noise, which frequently arises in practice, with clipping…

Machine Learning · Computer Science 2025-12-17 Chuan He