Related papers: RA-DCA: A Randomized Active-Set DCA for Directiona…

We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex…

Active learning improves the performance of machine learning methods by judiciously selecting a limited number of unlabeled data points to query for labels, with the aim of maximally improving the underlying classifier's performance. Recent…

We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and…

The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It…

We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

We present an active-set method for minimizing an objective that is the sum of a convex quadratic and $\ell_1$ regularization term. Unlike two-phase methods that combine a first-order active set identification step and a subspace phase…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical, as failure to do so can lead to catastrophic outcomes. Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate…

Imaging tasks are typically tackled using a structured optimization framework. This paper delves into a class of algorithms for difference-of-convex (DC) structured optimization, focusing on minimizing a DC function along with a possibly…

In the evolving landscape of mobile edge computing (MEC), enhancing communication reliability and computation efficiency to support increasingly stringent low-latency services remains a fundamental challenge. Rotatable antenna (RA) is a…

We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…

Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…

Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that…

Stochastic Dual Coordinate Ascent is a popular method for solving regularized loss minimization for the case of convex losses. In this paper we show how a variant of SDCA can be applied for non-convex losses. We prove linear convergence…