Related papers: On Riemannian Approach for Constrained Optimizatio…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Deep neural networks have shown impressive performance in supervised learning, enabled by their ability to fit well to the provided training data. However, their performance is largely dependent on the quality of the training data and often…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
This paper focuses on a class of binary orthogonal optimization problems frequently arising in semantic hashing. Consider that this class of problems may have an empty feasible set, rendering them not well-defined. We introduce an…
Label embedding is a framework for multiclass classification problems where each label is represented by a distinct vector of some fixed dimension, and training involves matching model output to the vector representing the correct label.…
In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in $x$ and…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
We propose a solution to the problem of estimating a Riemannian metric associated with a given differentiable manifold. The metric learning problem is based on minimizing the relative volume of a given set of points. We derive the details…
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…
Low-rank model compression is a widely used technique for reducing the computational load when training machine learning models. However, existing methods often rely on relaxing the low-rank constraint of the model weights using a…
We consider multi-label prediction problems with large output spaces under the assumption of output sparsity -- that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…