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The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we…

Machine Learning · Statistics 2017-07-07 HyoungSeok Kim , JiHoon Kang , WooMyoung Park , SukHyun Ko , YoonHo Cho , DaeSung Yu , YoungSook Song , JungWon Choi

Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…

Computation · Statistics 2022-03-01 Charles C. Margossian , Michael Betancourt

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…

Quantum Physics · Physics 2023-07-04 Y. S. Teo

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

Optimization and Control · Mathematics 2018-06-08 O. P. Ferreira , M. S. Louzeiro , L. F. Prudente

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly…

Machine Learning · Statistics 2013-01-08 David Wingate , Theophane Weber

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…

Optimization and Control · Mathematics 2023-03-01 Frank E. Curtis , Daniel P. Robinson , Baoyu Zhou

This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear…

Machine Learning · Computer Science 2024-10-25 Yuchen Zhu , Yufeng Zhang , Zhaoran Wang , Zhuoran Yang , Xiaohong Chen

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Optimization and Control · Mathematics 2025-08-05 Chenglong Bao , Liang Chen , Weizhi Shao

We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…

Machine Learning · Computer Science 2020-01-20 Goran Nakerst , John Brennan , Masudul Haque

Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where…

Optimization and Control · Mathematics 2016-11-17 Silvere Bonnabel

This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…

Optimization and Control · Mathematics 2021-10-29 Killian Wood , Gianluca Bianchin , Emiliano Dall'Anese

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Optimization and Control · Mathematics 2025-05-13 Naum Dimitrieski , Jing Cao , Christian Ebenbauer

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…

Numerical Analysis · Mathematics 2016-05-11 Emre Mengi , Emre Alper Yildirim , Mustafa Kilic

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…

Optimization and Control · Mathematics 2019-10-24 Brian Swenson , Anirudh Sridhar , H. Vincent Poor

We consider the problem of minimizing a convex function that depends on an uncertain parameter $\theta$. The uncertainty in the objective function means that the optimum, $x^*(\theta)$, is also a function of $\theta$. We propose an…

Optimization and Control · Mathematics 2022-07-06 Conor McMeel , Panos Parpas

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

Optimization and Control · Mathematics 2020-11-20 Kimon Antonakopoulos , E. Veronica Belmega , Panayotis Mertikopoulos

Gradient descent is a widely used iterative algorithm for finding local minima in multivariate functions. However, the final iterations often either overshoot the minima or make minimal progress, making it challenging to determine an…

Machine Learning · Computer Science 2024-10-28 Aviral Dhingra

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh