Related papers: Stochastic first-order methods: non-asymptotic and…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
This paper deals with the problem of accurately determining guaranteed suboptimal values of an unknown cost function on the basis of noisy measurements. We consider a set-valued variant to regression where, instead of finding a best…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization…
When optimizing problems with uncertain parameter values in a linear objective, decision-focused learning enables end-to-end learning of these values. We are interested in a stochastic scheduling problem, in which processing times are…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
Stochastic optimization methods encounter new challenges in the realm of streaming, characterized by a continuous flow of large, high-dimensional data. While first-order methods, like stochastic gradient descent, are the natural choice,…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
We present in this paper some worst-case datasets of deterministic first-order methods for solving large-scale binary logistic regression problems. Under the assumption that the number of algorithm iterations is much smaller than the…
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…
We examine fundamental tradeoffs in iterative distributed zeroth and first order stochastic optimization in multi-agent networks in terms of \emph{communication cost} (number of per-node transmissions) and \emph{computational cost},…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
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…