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Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

Numerical Analysis · Computer Science 2013-03-19 Bojana V. Rosić , Anna Kučerová , Jan Sýkora , Oliver Pajonk , Alexander Litvinenko , Hermann G. Matthies

Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…

Computation · Statistics 2019-08-16 Mark Huber

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Methodology · Statistics 2018-02-14 Daniela Calvetti , Matthew M. Dunlop , Erkki Somersalo , Andrew M. Stuart

Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…

Machine Learning · Statistics 2019-02-28 Xiaoyu Li , Francesco Orabona

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

Optimization and Control · Mathematics 2022-11-22 Weijia Shao , Fikret Sivrikaya , Sahin Albayrak

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

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

Optimization and Control · Mathematics 2021-10-05 Xiangyi Fan , Grani A. Hanasusanto

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…

General Mathematics · Mathematics 2017-07-03 Andrej Liptaj

Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…

Statistics Theory · Mathematics 2020-06-09 Julie Josse , Aude Sportisse , Claire Boyer , Aymeric Dieuleveut

We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…

Optimization and Control · Mathematics 2012-05-25 Sebastian U. Stich , Christian L. Müller , Bernd Gärtner

We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…

Optimization and Control · Mathematics 2023-07-21 Lei Qin , Michael Cantoni , Ye Pu

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…

Optimization and Control · Mathematics 2021-11-11 Theodoros Mamalis , Dusan Stipanovic , Petros Voulgaris

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

Signal Processing · Electrical Eng. & Systems 2020-07-10 Zhan Gao , Alec Koppel , Alejandro Ribeiro

In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed…

Computation · Statistics 2021-03-05 Nicholas Syring , Ryan Martin

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

Optimization and Control · Mathematics 2024-10-08 Albert S. Berahas , Miaolan Xie , Baoyu Zhou

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…

Optimization and Control · Mathematics 2023-01-09 Suyun Liu , Luis Nunes Vicente

Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in large-scale and high-dimensional problems in machine…

Machine Learning · Statistics 2025-01-22 Xiaoyu Wang , Mikolaj J. Kasprzak , Jeffrey Negrea , Solesne Bourguin , Jonathan H. Huggins

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Machine Learning · Computer Science 2020-03-04 Achraf Bahamou , Donald Goldfarb

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

Optimization and Control · Mathematics 2013-01-08 Enlu Zhou , Jiaqiao Hu

Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying…

Optimization and Control · Mathematics 2024-10-28 Sheheryar Mehmood , Peter Ochs