Related papers: A multi-fidelity adaptive dynamical low-rank based…

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure. Such instance-specific behavior is not captured by existing global minimax…

Recommendation systems often rely on point-wise loss metrics such as the mean squared error. However, in real recommendation settings only few items are presented to a user. This observation has recently encouraged the use of rank-based…

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

When using reinforcement learning (RL) algorithms it is common, given a large state space, to introduce some form of approximation architecture for the value function (VF). The exact form of this architecture can have a significant effect…

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition…

Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$…

The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq…

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional…

In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank.…

Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…

This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac-Frenkel…

Using a Wigner Lorentzian Random Matrix ensemble, we study the fidelity, $F(t)$, of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes…

The stochastic description of chemical reaction networks with the kinetic chemical master equation (CME) is important for studying biological cells, but it suffers from the curse of dimensionality: The amount of data to be stored grows…