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This work studies online zero-order optimization of convex and Lipschitz functions. We present a novel gradient estimator based on two function evaluations and randomization on the $\ell_1$-sphere. Considering different geometries of…

Statistics Theory · Mathematics 2022-09-21 Arya Akhavan , Evgenii Chzhen , Massimiliano Pontil , Alexandre B. Tsybakov

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…

Machine Learning · Statistics 2025-09-03 Arya Akhavan , Alexandre B. Tsybakov

We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…

Machine Learning · Computer Science 2022-11-28 Arya Akhavan , Massimiliano Pontil , Alexandre B. Tsybakov

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

Optimization and Control · Mathematics 2024-03-27 Shuyao Li , Stephen J. Wright

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

Optimization and Control · Mathematics 2026-04-02 Albert S. Berahas , Frank E. Curtis , Lara Zebiane

Frequently, when dealing with many machine learning models, optimization problems appear to be challenging due to a limited understanding of the constructions and characterizations of the objective functions in these problems. Therefore,…

Optimization and Control · Mathematics 2024-11-27 A. V. Gasnikov , M. S. Alkousa , A. V. Lobanov , Y. V. Dorn , F. S. Stonyakin , I. A. Kuruzov , S. R. Singh

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use the Gaussian smoothing approach of Nesterov and Spokoiny [2015] and extend…

Optimization and Control · Mathematics 2021-01-14 Innokentiy Shibaev , Pavel Dvurechensky , Alexander Gasnikov

This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…

Optimization and Control · Mathematics 2023-11-29 Pham Duy Khanh , Boris S. Mordukhovich , Dat Ba Tran

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…

Machine Learning · Computer Science 2016-05-27 Francis Bach , Vianney Perchet

We present a novel gradient-free algorithm to solve a convex stochastic optimization problem, such as those encountered in medicine, physics, and machine learning (e.g., adversarial multi-armed bandit problem), where the objective function…

Optimization and Control · Mathematics 2024-11-22 Georgii Bychkov , Darina Dvinskikh , Anastasia Antsiferova , Alexander Gasnikov , Aleksandr Lobanov

We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…

Optimization and Control · Mathematics 2022-10-11 Tesi Xiao , Krishnakumar Balasubramanian , Saeed Ghadimi

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

Optimization and Control · Mathematics 2026-04-10 Huaiyi Mu , Yujie Tang , Jie Song , Zhongkui Li

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…

Computation · Statistics 2025-12-04 Christophe Andrieu , Nicolas Chopin , Ettore Fincato , Mathieu Gerber

Polyak-{\L}ojasiewicz (PL) [Polyak, 1963] condition is a weaker condition than the strong convexity but suffices to ensure a global convergence for the Gradient Descent algorithm. In this paper, we study the lower bound of algorithms using…

Optimization and Control · Mathematics 2023-08-03 Pengyun Yue , Cong Fang , Zhouchen Lin

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…

Machine Learning · Computer Science 2022-09-13 Srujan Teja Thomdapu , Harshvardhan , Ketan Rajawat

In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…

Optimization and Control · Mathematics 2022-09-13 Aleksandr Beznosikov , Abdurakhmon Sadiev , Alexander Gasnikov

First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…

Optimization and Control · Mathematics 2024-04-30 Mihai I. Florea , Yurii Nesterov

We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…

Optimization and Control · Mathematics 2025-01-29 Zhenwei Lin , Jingfan Xia , Qi Deng , Luo Luo

We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…

Optimization and Control · Mathematics 2023-03-28 Darina Dvinskikh , Vladislav Tominin , Yaroslav Tominin , Alexander Gasnikov

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
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