English
Related papers

Related papers: High-Probability Guarantees for Random Zeroth-Orde…

200 papers

In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilvel problems, when neither the upper/lower objective values, nor their unbiased gradient estimates are available. In particular, exploiting…

Optimization and Control · Mathematics 2024-04-02 Alireza Aghasi , Saeed Ghadimi

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…

Machine Learning · Computer Science 2020-05-20 Daniel Golovin , John Karro , Greg Kochanski , Chansoo Lee , Xingyou Song , Qiuyi Zhang

We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…

Optimization and Control · Mathematics 2026-01-14 Mert Gürbüzbalaban , Yasa Syed , Necdet Serhat Aybat

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

We present two easy-to-implement gradient-free/zeroth-order methods to optimize a stochastic non-smooth function accessible only via a black-box. The methods are built upon efficient first-order methods in the heavy-tailed case, i.e., when…

Optimization and Control · Mathematics 2023-08-25 Nikita Kornilov , Alexander Gasnikov , Pavel Dvurechensky , Darina Dvinskikh

We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…

Optimization and Control · Mathematics 2026-04-17 Hengxu Yu , Xiao Li

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

Optimization and Control · Mathematics 2019-04-23 Qiuwei Li , Zhihui Zhu , Gongguo Tang , Michael B. Wakin

In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…

Optimization and Control · Mathematics 2020-02-20 V. Kungurtsev , F. Rinaldi

Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…

Optimization and Control · Mathematics 2024-07-16 Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based…

Machine Learning · Computer Science 2026-04-01 Kaustubh Kartikey , Shalabh Bhatnagar

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Optimization and Control · Mathematics 2016-05-30 James Renegar

Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search…

Machine Learning · Statistics 2018-08-03 Liu Liu , Minhao Cheng , Cho-Jui Hsieh , Dacheng Tao

We propose an adaptive zeroth-order method for minimizing differentiable functions with $L$-Lipschitz continuous gradients. The method is designed to take advantage of the eventual compressibility of the gradient of the objective function,…

Optimization and Control · Mathematics 2025-07-16 Geovani Nunes Grapiglia , Daniel McKenzie

The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…

Optimization and Control · Mathematics 2025-05-05 Shotaro Yagishita

We establish generic uniform convergence guarantees for Gaussian data in terms of the Rademacher complexity of the hypothesis class and the Lipschitz constant of the square root of the scalar loss function. We show how these guarantees…

Machine Learning · Statistics 2023-06-26 Lijia Zhou , Zhen Dai , Frederic Koehler , Nathan Srebro

We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and H\"older continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It…

Optimization and Control · Mathematics 2026-01-05 Naoki Marumo , Akiko Takeda

We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main…

Optimization and Control · Mathematics 2021-01-06 Jiaxiang Li , Krishnakumar Balasubramanian , Shiqian Ma

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…

Optimization and Control · Mathematics 2022-06-22 Kimon Antonakopoulos , Dong Quan Vu , Vokan Cevher , Kfir Y. Levy , Panayotis Mertikopoulos

In this paper, we study an explicit Tikhonov-regularized inertial gradient algorithm for smooth convex minimization with Lipschitz continuous gradient. The method is derived via an explicit time discretization of a damped inertial system…

Optimization and Control · Mathematics 2026-02-02 Samir Adly , Vinh Thanh Ho , Huu Nhan Nguyen

The analysis of gradient descent-type methods typically relies on the Lipschitz continuity of the objective gradient. This generally requires an expensive hyperparameter tuning process to appropriately calibrate a stepsize for a given…

Optimization and Control · Mathematics 2023-11-16 Albert S. Berahas , Lindon Roberts , Fred Roosta