Related papers: A Local Lemma for Focused Stochastic Algorithms

Machine Learning algorithms have been extensively researched throughout the last decade, leading to unprecedented advances in a broad range of applications, such as image classification and reconstruction, object recognition, and text…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants bias their sampling using various…

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…

Fine-tuning a general-purpose large language model (LLM) for a specific domain or task has become a routine procedure for ordinary users. However, fine-tuning is known to remove the safety alignment features of the model, even when the…

Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on…

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical…

In this paper, we develop a \textcolor{black}{\emph{distributed}} algorithm to localize a network of robots moving arbitrarily in a bounded region. In the case of such mobile networks, the main challenge is that the robots may not be able…

Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in…

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…

Large language models (LLMs) offer substantial promise for text classification in political science, yet their effectiveness often depends on high-quality prompts and exemplars. To address this, we introduce a three-stage framework that…

Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the best algorithm in the literature for solving this problem. In light…

As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…

Optimization algorithms are widely employed to tackle complex problems, but designing them manually is often labor-intensive and requires significant expertise. Global placement is a fundamental step in electronic design automation (EDA).…

State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…

First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…

Pseudo-Boolean Optimization (PBO) provides a powerful framework for modeling combinatorial problems through pseudo-Boolean (PB) constraints. Local search solvers have shown excellent performance in PBO solving, and their efficiency is…

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Thematic analysis and other variants of inductive coding are widely used qualitative analytic methods within empirical legal studies (ELS). We propose a novel framework facilitating effective collaboration of a legal expert with a large…