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Related papers: Stochastic first-order methods: non-asymptotic and…

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In this work, to efficiently help escape the stationary and saddle points, we propose, analyze, and generalize a stochastic strategy performed as an operator for a first-order gradient descent algorithm in order to increase the target…

Machine Learning · Computer Science 2022-05-23 Wei Zhang , Yu Bao

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

Optimization and Control · Mathematics 2019-10-10 Andrei Kulunchakov , Julien Mairal

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…

Optimization and Control · Mathematics 2023-03-28 Albert S. Berahas , Jiahao Shi , Zihong Yi , Baoyu Zhou

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Optimization and Control · Mathematics 2020-03-10 Ion Necoara

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…

Optimization and Control · Mathematics 2025-05-28 Francesco Cordiano , Matin Jafarian , Bart De Schutter

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…

Optimization and Control · Mathematics 2019-03-29 Prashanth L A , Shalabh Bhatnagar , Nirav Bhavsar , Michael Fu , Steven I. Marcus

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

Machine Learning · Computer Science 2017-01-31 Diederik P. Kingma , Jimmy Ba

This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…

Optimization and Control · Mathematics 2025-02-27 Rajmadan Lakshmanan , Alois Pichler , Miloš Kopa

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

Optimization and Control · Mathematics 2011-08-30 Alexandre d'Aspremont

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

Optimization and Control · Mathematics 2018-03-12 Andre Milzarek , Xiantao Xiao , Shicong Cen , Zaiwen Wen , Michael Ulbrich

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

Optimization and Control · Mathematics 2021-05-31 C. Cartis , N. I. M. Gould , Ph. L. Toint

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

Optimization and Control · Mathematics 2023-10-04 Baptiste Goujaud , Aymeric Dieuleveut , Adrien Taylor

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…

Optimization and Control · Mathematics 2023-01-27 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

Optimization and Control · Mathematics 2020-05-05 Andrei Patrascu

Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…

Optimization and Control · Mathematics 2021-06-30 Mathieu Barré , Adrien Taylor , Francis Bach

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…

Optimization and Control · Mathematics 2024-07-23 William G. Powell , Hanbaek Lyu

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use…

Systems and Control · Electrical Eng. & Systems 2022-07-19 Henning Schlüter , Frank Allgöwer

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

Numerical Analysis · Mathematics 2020-09-15 Stefania Bellavia , Gianmarco Gurioli