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Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…

Numerical Analysis · Mathematics 2025-02-26 El-Mehdi El Arar , Massimiliano Fasi , Silviu-Ioan Filip , Mantas Mikaitis

The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…

Machine Learning · Computer Science 2017-09-15 Elad Hazan , Haipeng Luo

We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…

Machine Learning · Computer Science 2019-02-26 Peter L. Bartlett , Victor Gabillon , Michal Valko

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…

Optimization and Control · Mathematics 2019-12-05 Wenjie Huang , William B. Haskell

Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…

Optimization and Control · Mathematics 2020-12-29 Mingrui Liu , Youssef Mroueh , Jerret Ross , Wei Zhang , Xiaodong Cui , Payel Das , Tianbao Yang

We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…

Machine Learning · Computer Science 2020-11-04 Rémi Jézéquel , Pierre Gaillard , Alessandro Rudi

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…

Optimization and Control · Mathematics 2019-02-04 Olivier Fercoq , Ahmet Alacaoglu , Ion Necoara , Volkan Cevher

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Optimization and Control · Mathematics 2020-12-15 Dmitriy Drusvyatskiy , Lin Xiao

We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the…

Optimization and Control · Mathematics 2022-06-28 Ahmed Attia , Sven Leyffer , Todd Munson

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

Optimization and Control · Mathematics 2020-09-10 Hamed Hassani , Amin Karbasi , Aryan Mokhtari , Zebang Shen

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…

Numerical Analysis · Mathematics 2012-07-27 David Lawlor , Yang Wang , Andrew Christlieb

We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…

Machine Learning · Statistics 2024-03-26 Kody Law , Neil Walton , Shangda Yang

Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptive Galerkin FE method for linear parametric PDEs with…

Numerical Analysis · Mathematics 2018-11-02 Martin Eigel , Manuel Marschall , Max Pfeffer , Reinhold Schneider

OBDD-based graph algorithms deal with the characteristic function of the edge set E of a graph $G = (V,E)$ which is represented by an OBDD and solve optimization problems by mainly using functional operations. We present an OBDD-based…

Data Structures and Algorithms · Computer Science 2015-04-16 Marc Bury

To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log(N)) operations and O(log(N)) active memory, in place of O(N^2)…

Numerical Analysis · Mathematics 2007-05-23 María López-Fernández , Christian Lubich , Achim Schädle

We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision…

Optimization and Control · Mathematics 2018-08-17 Lijun Ding , Madeleine Udell

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

Optimization and Control · Mathematics 2019-02-28 S. Gratton , E. Simon , Ph. L. Toint

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…

Data Structures and Algorithms · Computer Science 2024-09-12 Sander Borst , Daniel Dadush , Sophie Huiberts , Danish Kashaev

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…

Machine Learning · Statistics 2020-09-07 Andrei Kulunchakov , Julien Mairal

In this paper, we introduce EvoPort, a novel evolutionary portfolio optimization method that leverages stochastic exploration over a spectrum of investment pipeline depths. From raw equity data, we employ a randomized feature generation…

Computation · Statistics 2025-06-11 Nguyen Van Thanh , Nguyen Thi Hau