Related papers: LRSVRG-IMC: An SVRG-Based Algorithm for LowRank In…
We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
In this paper, we propose a novel reinforcement- learning algorithm consisting in a stochastic variance-reduced version of policy gradient for solving Markov Decision Processes (MDPs). Stochastic variance-reduced gradient (SVRG) methods…
Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Iterative learning control (ILC) is a powerful technique for high performance tracking in the presence of modeling errors for optimal control applications. There is extensive prior work showing its empirical effectiveness in applications…
Incomplete multiview clustering (IMVC) has gained significant attention for its effectiveness in handling missing sample challenges across various views in real-world multiview clustering applications. Most IMVC approaches tackle this…
We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware…
Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
In this paper, we study a class of fractional optimization problems, in which the numerator of the objective is the sum of a convex function and a differentiable function with a Lipschitz continuous gradient, while the denominator is a…
The theory of greedy low-rank learning (GLRL) aims to explain the impressive generalization capabilities of deep learning. It proves that stochastic gradient-based training implicitly regularizes neural networks towards low-rank solutions…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…
Fine-grained visual categorization (FGVC) is a challenging task due to similar visual appearances between various species. Previous studies always implicitly assume that the training and test data have the same underlying distributions, and…
We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…
In financial predictions, the performance of machine learning models is often assessed by Rank IC, which is the Spearman rank correlation between the model predictions and the realized asset returns. Despite its wide adoption, most existing…
Autonomous Mobile Robots (AMRs) have become indispensable in industrial applications due to their operational flexibility and efficiency. Navigation serves as a crucial technical foundation for accomplishing complex tasks. However,…
Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regression matrix to effectively capture the intrinsic structure…