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The vast majority of convergence rates analysis for stochastic gradient methods in the literature focus on convergence in expectation, whereas trajectory-wise almost sure convergence is clearly important to ensure that any instantiation of…

Machine Learning · Computer Science 2022-07-12 Jun Liu , Ye Yuan

In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, for the problem of minimizing a class of convex objective…

Optimization and Control · Mathematics 2017-12-19 Yi Zhou , Yingbin Liang , Lixin Shen

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…

Optimization and Control · Mathematics 2015-09-16 Qi Deng , Guanghui Lan , Anand Rangarajan

Backtracking linesearch is the de facto approach for minimizing continuously differentiable functions with locally Lipschitz gradient. In recent years, it has been shown that in the convex setting it is possible to avoid linesearch…

Optimization and Control · Mathematics 2024-03-14 Puya Latafat , Andreas Themelis , Lorenzo Stella , Panagiotis Patrinos

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

Optimization and Control · Mathematics 2017-05-23 Xiao Wang , Shiqian Ma , Donald Goldfarb , Wei Liu

We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…

Machine Learning · Computer Science 2025-02-06 Ségolène Martin , Jean-Christophe Pesquet , Gabriele Steidl , Ismail Ben Ayed

Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical…

Optimization and Control · Mathematics 2018-11-05 Clarice Poon , Jingwei Liang , Carola-Bibiane Schönlieb

Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- common in modern machine learning and reinforcement learning -- remains poorly understood. In this…

Optimization and Control · Mathematics 2025-08-08 Ilyas Fatkhullin , Florian Hübler , Guanghui Lan

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

Optimization and Control · Mathematics 2025-11-19 Vitaliano S. Amaral , Marcio Antônio de A. Bortoloti , Jurandir O. Lopes , Gilson N. Silva

In this paper, we focus on the decentralized stochastic subgradient-based methods in minimizing nonsmooth nonconvex functions without Clarke regularity, especially in the decentralized training of nonsmooth neural networks. We propose a…

Optimization and Control · Mathematics 2026-01-07 Siyuan Zhang , Nachuan Xiao , Xin Liu

Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for example the learning rate) of the algorithm. In this paper we…

Optimization and Control · Mathematics 2019-07-15 Adam M. Oberman , Mariana Prazeres

In this paper, we combine the positive aspects of the Gradient Sampling (GS) and bundle methods, as the most efficient methods in nonsmooth optimization, to develop a robust method for solving unconstrained nonsmooth convex optimization…

Optimization and Control · Mathematics 2019-11-26 M. Maleknia , M. Shamsi

In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…

Machine Learning · Computer Science 2015-12-08 Lijun Zhang , Tianbao Yang , Rong Jin , Zhi-Hua Zhou

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Machine Learning · Computer Science 2018-02-02 Tianyi Lin , Linbo Qiao , Teng Zhang , Jiashi Feng , Bofeng Zhang

Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…

Machine Learning · Computer Science 2023-06-06 Amirhossein Reisizadeh , Haochuan Li , Subhro Das , Ali Jadbabaie

Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…

Machine Learning · Computer Science 2025-02-25 Kart-Leong Lim , Xudong Jiang

Variance reduced stochastic gradient (SGD) methods converge significantly faster than the vanilla SGD counterpart. However, these methods are not very practical on large scale problems, as they either i) require frequent passes over the…

Optimization and Control · Mathematics 2018-10-17 Anant Raj , Sebastian U. Stich

The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…

Optimization and Control · Mathematics 2026-03-04 Junwen Qiu , Li Jiang , Andre Milzarek

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of…

Signal Processing · Electrical Eng. & Systems 2018-04-24 Aven Samareh , Mahshid Salemi Parizi