Related papers: Rethinking Hard Thresholding Pursuit: Full Adaptat…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
The Iterative Hard Thresholding (IHT) algorithm has been considered extensively as an effective deterministic algorithm for solving sparse optimizations. The IHT algorithm benefits from the information of the batch (full) gradient at each…
Orthogonal matching pursuit (OMP) is a greedy algorithm popularly being used for the recovery of sparse signals. In this paper, we study the performance of OMP for support recovery of sparse signal under noise. Our analysis shows that under…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…
Consider nonparametric function estimation under $L^p$-loss. The minimax rate for estimation of the regression function over a H\"older ball with smoothness index $\beta$ is $n^{-\beta/(2\beta+1)}$ if $1\leq p<\infty$ and $(n/\log…
We introduce a generic template for developing regret minimization algorithms in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal regret as long as certain properties are ensured. The key of our analysis is a new…
This work focuses on the problem of hyper-parameter tuning (HPT) for robust (i.e., adversarially trained) models, shedding light on the new challenges and opportunities arising during the HPT process for robust models. To this end, we…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Linear inverse problems arise in diverse engineering fields especially in signal and image reconstruction. The development of computational methods for linear inverse problems with sparsity is one of the recent trends in this field. The…
In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
Data-intensive scientific and commercial applications increasingly require frequent movement of large datasets from one site to the other(s). Despite growing network capacities, these data movements rarely achieve the promised data transfer…
We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating…
In the measurement-constrained problems, despite the availability of large datasets, we may be only affordable to observe the labels on a small portion of the large dataset. This poses a critical question that which data points are most…
Packing for Supervised Fine-Tuning (SFT) in autoregressive models involves concatenating data points of varying lengths until reaching the designed maximum length to facilitate GPU processing. However, randomly concatenating data points can…