Related papers: Scalable Frank-Wolfe on Generalized Self-concordan…
This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make…
Forward stagewise regression follows a very simple strategy for constructing a sequence of sparse regression estimates: it starts with all coefficients equal to zero, and iteratively updates the coefficient (by a small amount $\epsilon$) of…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
Shuffling gradient methods are widely used in modern machine learning tasks and include three popular implementations: Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG). Compared to the empirical success, the…
The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…
We propose a fast and scalable Polyatomic Frank-Wolfe (P-FW) algorithm for the resolution of high-dimensional LASSO regression problems. The latter improves upon traditional Frank-Wolfe methods by considering generalized greedy steps with…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…
Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent's textbook $LD^2/2T$ convergence guarantees can be improved by constant factors, conjecturing an accelerated rate strictly…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming…
Frank-Wolfe algorithms have recently regained the attention of the Machine Learning community. Their solid theoretical properties and sparsity guarantees make them a suitable choice for a wide range of problems in this field. In addition,…
We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given…
Performative reinforcement learning is an emerging dynamical decision making framework, which extends reinforcement learning to the common applications where the agent's policy can change the environmental dynamics. Existing works on…
To efficiently solve online problems with complicated constraints, projection-free algorithms including online frank-wolfe (OFW) and its variants have received significant interest recently. However, in the general case, existing efficient…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
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…