Related papers: Stochastic Frank-Wolfe for Composite Convex Minimi…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
In this paper, we consider a class of stochastic optimization problems over the expectation-formulated generalized Stiefel manifold (SOEGS), where the objective function $f$ is continuously differentiable. We propose a novel constraint…
Several attempts to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic…
In this paper, we consider non-convex optimization problems under \textit{unknown} yet safety-critical constraints. Such problems naturally arise in a variety of domains including robotics, manufacturing, and medical procedures, where it is…
The Frank-Wolfe algorithm has seen a resurgence in popularity due to its ability to efficiently solve constrained optimization problems in machine learning and high-dimensional statistics. As such, there is much interest in establishing…
We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X =…
Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified…
In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…
Frank-Wolfe methods are popular for optimization over a polytope. One of the reasons is because they do not need projection onto the polytope but only linear optimization over it. To understand its complexity, Lacoste-Julien and Jaggi…
In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model.…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
The analysis of Frank Wolfe (FW) variants is often complicated by the presence of different kinds of "good" and "bad" steps. In this article we aim to simplify the convergence analysis of some of these variants by getting rid of such a…
This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…