Related papers: Primal-dual algorithm for contextual stochastic co…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods,…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…
Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…
This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost…
Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…
We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…
We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates…
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…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…
Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…
We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main…
We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…