Related papers: L-SR1: Learned Symmetric-Rank-One Preconditioning

Multimodal Large Language Models (MLLMs) have gained significant traction for their ability to process diverse input data types and generate coherent, contextually relevant outputs across various applications. While supervised fine-tuning…

It is a challenging problem that solving the \textit{multivariate linear model} (MLM) $\mathbf{A}\mathbf{x}=\mathbf{b}$ with the $\ell_1 $-norm approximation method such that $||\mathbf{A}\mathbf{x}-\mathbf{b}||_1$, the $\ell_1$-norm of the…

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

Many types of neural network layers rely on matrix properties such as invertibility or orthogonality. Retaining such properties during optimization with gradient-based stochastic optimizers is a challenging task, which is usually addressed…

Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose…

In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers…

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly…

Current end-to-end deep Reinforcement Learning (RL) approaches require jointly learning perception, decision-making and low-level control from very sparse reward signals and high-dimensional inputs, with little capability of incorporating…

Self-paced reinforcement learning (RL) aims to improve the data efficiency of learning by automatically creating sequences, namely curricula, of probability distributions over contexts. However, existing techniques for self-paced RL fail in…

This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…

Ensuring reliability in modern software systems requires rigorous pre-production testing across highly heterogeneous and evolving environments. Because exhaustive evaluation is infeasible, practitioners must decide how to allocate limited…

The ongoing decarbonisation of power systems is driving an increasing reliance on distributed energy resources, which introduces complex and nonlinear interactions that are difficult to capture in conventional optimisation models. As a…

Existing robot video world models are typically trained with low-level objectives such as reconstruction and perceptual similarity, which are poorly aligned with the capabilities that matter most for robot decision making, including…

Recent works on large language models (LLMs) have successfully demonstrated the emergence of reasoning capabilities via reinforcement learning (RL). Although recent efforts leverage group relative policy optimization (GRPO) for MLLMs…

This paper presents a novel reinforcement learning (RL) framework for dynamically optimizing numerical precision in the preconditioned conjugate gradient (CG) method. By modeling precision selection as a Markov Decision Process (MDP), we…

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…

We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously…