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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

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

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

Optimization and Control · Mathematics 2026-04-02 Khanh-Hung Giang-Tran , Soroosh Shafiee , Nam Ho-Nguyen

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…

Optimization and Control · Mathematics 2019-05-31 Hakan Gokcesu , Kaan Gokcesu , Suleyman Serdar Kozat

Recent applications in machine learning have renewed the interest of the community in min-max optimization problems. While gradient-based optimization methods are widely used to solve such problems, there are however many scenarios where…

Optimization and Control · Mathematics 2021-04-15 Sotiris Anagnostidis , Aurelien Lucchi , Youssef Diouane

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…

Optimization and Control · Mathematics 2022-01-05 Enrico Bettiol , Christoph Buchheim , Marianna De Santis , Francesco Rinaldi

Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…

Optimization and Control · Mathematics 2021-05-12 Hassan Rafique , Mingrui Liu , Qihang Lin , Tianbao Yang

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…

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

Optimization and Control · Mathematics 2024-11-27 O. S. Savchuk , M. S. Alkousa , A. S. Shushko , A. A. Vyguzov , F. S. Stonyakin , D. A. Pasechnyuk , A. V. Gasnikov

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

Optimization and Control · Mathematics 2023-07-25 Le Thi Khanh Hien , Renbo Zhao , William B. Haskell

In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk…

Data Structures and Algorithms · Computer Science 2017-07-12 Hugo Gilbert , Olivier Spanjaard

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

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

Optimization and Control · Mathematics 2023-07-19 Renbo Zhao

Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…

Machine Learning · Computer Science 2024-09-11 Yuma Ichikawa , Koji Hukushima

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

In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible…

Optimization and Control · Mathematics 2023-08-16 Jannis Kurtz

Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc. For these problems, gradient-based methods are well understood and enjoy strong guarantees. However, in the absence of convexity or…

Optimization and Control · Mathematics 2026-05-26 Chinmay Maheshwari , Chinmay Pimpalkhare , Debasish Chatterjee

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

Optimization and Control · Mathematics 2026-03-31 Guido Tapia-Riera , Camille Castera , Nicolas Papadakis

The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal…

Optimization and Control · Mathematics 2021-03-17 Songtao Lu , Ioannis Tsaknakis , Mingyi Hong , Yongxin Chen

This work is devoted to solving the composite optimization problem with the mixture oracle: for the smooth part of the problem, we have access to the gradient, and for the non-smooth part, only the one-point zero-order oracle is available.…

Optimization and Control · Mathematics 2025-07-23 Aleksandr Beznosikov , Ivan Stepanov , Artyom Voronov , Alexander Gasnikov