Related papers: High-dimensional Optimization with Low Rank Tensor…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…

This paper studies decentralized optimization over a compact submanifold within a communication network of $n$ nodes, where each node possesses a smooth non-convex local cost function, and the goal is to jointly minimize the sum of these…

Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based…

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, with more spectral bands for HSI, while the running time of these methods significantly…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…

In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…

We consider the challenge of black-box optimization within hybrid discrete-continuous and variable-length spaces, a problem that arises in various applications, such as decision tree learning and symbolic regression. We propose DisCo-DSO…

In this article we consider min-min type of problems or minimization by two groups of variables. Min-min problems may occur in case if some groups of variables in convex optimization have different dimensions or if these groups have…

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…

There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate.…