Related papers: Stochastic Zeroth-order Optimization in High Dimen…
It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…
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…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some…
The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
Stochastic optimization problems with unknown decision-dependent distributions have attracted increasing attention in recent years due to its importance in applications. Since the gradient of the objective function is inaccessible as a…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Zeroth-order optimization (ZOO) is an important framework for stochastic optimization when gradients are unavailable or expensive to compute. A potential limitation of existing ZOO methods is the bias inherent in most gradient estimators…
$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…