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We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

This work considers minimizing a sum of convex functions, each with potentially different structure ranging from nonsmooth to smooth, Lipschitz to non-Lipschitz. Nesterov's universal fast gradient method provides an optimal black-box…

Optimization and Control · Mathematics 2023-06-14 Benjamin Grimmer

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods…

Optimization and Control · Mathematics 2021-12-22 Zichong Li , Pin-Yu Chen , Sijia Liu , Songtao Lu , Yangyang Xu

In this work we address the problem of convex optimization in a multi-agent setting where the objective is to minimize the mean of local cost functions whose derivatives are not available (e.g. black-box models). Moreover agents can only…

Optimization and Control · Mathematics 2023-06-14 Alessio Maritan , Luca Schenato

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

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. One of the predominant approaches…

Optimization and Control · Mathematics 2022-08-22 Wouter Jongeneel

Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…

Optimization and Control · Mathematics 2024-07-17 Matthias J. Ehrhardt , Erlend S. Riis , Torbjørn Ringholm , Carola-Bibiane Schönlieb

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Optimization and Control · Mathematics 2024-04-16 Guy Kornowski , Ohad Shamir

We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…

Optimization and Control · Mathematics 2021-11-16 David Kozak , Cesare Molinari , Lorenzo Rosasco , Luis Tenorio , Silvia Villa

We consider a class of structured, nonconvex, nonsmooth optimization problems under orthogonality constraints, where the objectives combine a smooth function, a nonsmooth concave function, and a nonsmooth weakly convex function. This class…

Optimization and Control · Mathematics 2025-01-14 Ganzhao Yuan

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

Optimization and Control · Mathematics 2025-11-14 Ilyas Fatkhullin , Niao He , Guanghui Lan , Florian Wolf

Standard approaches to stochastic gradient estimation, with only noisy black-box function evaluations, use the finite-difference method or its variants. While natural, it is open to our knowledge whether their statistical accuracy is the…

Statistics Theory · Mathematics 2020-11-13 Henry Lam , Haidong Li , Xuhui Zhang

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

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…

Machine Learning · Computer Science 2025-08-08 Ashok Cutkosky , Harsh Mehta , Francesco Orabona

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…

Optimization and Control · Mathematics 2019-01-16 Krishnakumar Balasubramanian , Saeed Ghadimi

Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow…

Machine Learning · Computer Science 2025-05-26 Sihwan Park , Jihun Yun , SungYub Kim , Souvik Kundu , Eunho Yang

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

Optimization and Control · Mathematics 2025-01-14 Raghu Bollapragada , Cem Karamanli

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Optimization and Control · Mathematics 2025-04-21 Spyridon Pougkakiotis , Dionysios S. Kalogerias

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…

Optimization and Control · Mathematics 2025-12-25 Junpeng Zhou , Na Zhang , Qia Li