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We investigate the uniform convergence of subdifferential mappings from empirical risk to population risk in nonsmooth, nonconvex stochastic optimization. This question is key to understanding how empirical stationary points approximate…

Optimization and Control · Mathematics 2025-08-26 Feng Ruan

This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…

Optimization and Control · Mathematics 2025-05-26 Aleksandr Lobanov , Alexander Gasnikov

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

Machine Learning · Computer Science 2026-05-12 Johannes Teutsch , Oleksii Molodchyk , Marion Leibold , Timm Faulwasser , Armin Lederer

This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…

Optimization and Control · Mathematics 2026-04-16 Chenyang Qiu , Mihitha Maithripala , Zongli Lin

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

Optimization and Control · Mathematics 2022-10-31 Dennis J. Marquis , Dany Abou Jaoude , Mazen Farhood , Craig A. Woolsey

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

We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…

Optimization and Control · Mathematics 2026-05-08 Nicholas Pischke , Thomas Powell

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 stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…

Optimization and Control · Mathematics 2014-03-25 Farzad Yousefian , Angelia Nedic , Uday V. Shanbhag

We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the…

Machine Learning · Computer Science 2018-10-26 Wonyeol Lee , Hangyeol Yu , Hongseok Yang

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

Functional Analysis · Mathematics 2014-03-14 Ibrahim Karahan , Murat Ozdemir

We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…

Computation · Statistics 2014-01-10 Tim Salimans

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…

Optimization and Control · Mathematics 2020-11-13 Eduard Gorbunov , Darina Dvinskikh , Alexander Gasnikov

In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a root of a co-coercive operator), a central problem in…

Optimization and Control · Mathematics 2025-12-16 Nghia Nguyen-Trung , Quoc Tran-Dinh

The monotone variational inequality is a central problem in mathematical programming that unifies and generalizes many important settings such as smooth convex optimization, two-player zero-sum games, convex-concave saddle point problems,…

Optimization and Control · Mathematics 2022-05-17 Yang Cai , Argyris Oikonomou , Weiqiang Zheng

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is thoroughly…

Optimization and Control · Mathematics 2015-04-20 Patrick L. Combettes , Jean-Christophe Pesquet

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

Machine Learning · Computer Science 2026-05-26 Natanael Alpay , Emeric Battaglia

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…

Machine Learning · Statistics 2016-08-15 Mohammad Emtiyaz Khan , Reza Babanezhad , Wu Lin , Mark Schmidt , Masashi Sugiyama

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…

Optimization and Control · Mathematics 2025-05-28 Ling Liang , Zusen Xu , Kim-Chuan Toh , Jia-Jie Zhu