Related papers: AK-SLRL: Adaptive Krylov Subspace Exploration Usin…

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method…

Deep reinforcement learning (DRL) algorithms have proven effective in robot navigation, especially in unknown environments, by directly mapping perception inputs into robot control commands. However, most existing methods ignore the local…

Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been…

It is challenging to recover the large-scale internet traffic data purely from the link measurements. With the rapid growth of the problem scale, it will be extremely difficult to sustain the recovery accuracy and the computational cost. In…

Safe Reinforcement Learning (SRL) aims to realize a safe learning process for Deep Reinforcement Learning (DRL) algorithms by incorporating safety constraints. However, the efficacy of SRL approaches often relies on accurate function…

The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…

Augmented Krylov subspace methods aid in accelerating the convergence of a standard Krylov subspace method by including additional vectors in the search space. A residual projection framework based on residual (Petrov-) Galerkin constraints…

For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…

On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of $s$-step Krylov subspace method variants, in which iterations are…

Sparse structures are widely recognized and utilized in channel estimation. Two typical mechanisms, namely proportionate updating (PU) and zero-attracting (ZA) techniques, achieve better performance, but their computational complexity are…

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Reinforcement Learning (RL) has become essential for eliciting complex reasoning capabilities in Large Language Models (LLMs). However, the substantial memory overhead of storing Key-Value (KV) caches during long-horizon rollouts acts as a…

Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has emerged as a promising technology to realize full-space coverage and boost spectral efficiency in next-generation wireless networks. Yet, the joint…

It is well known that for general linear systems, only optimal Krylov methods with long recurrences exist. For special classes of linear systems it is possible to find optimal Krylov methods with short recurrences. In this paper we consider…

LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and…

Although the sparse multinomial logistic regression (SMLR) has provided a useful tool for sparse classification, it suffers from inefficacy in dealing with high dimensional features and manually set initial regressor values. This has…

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…

This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand…

In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…