Related papers: VAMO: Efficient Zeroth-Order Variance Reduction fo…
Large language models (LLMs) have demonstrated impressive capabilities across numerous NLP tasks. Nevertheless, conventional first-order fine-tuning techniques impose heavy memory demands, creating practical obstacles to real-world…
Fine-tuning pre-trained Large Language Models (LLMs) for downstream tasks using First-Order (FO) optimizers presents significant computational challenges. Parameter-Efficient Fine-Tuning (PEFT) methods address these by freezing most model…
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…
Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive.…
Visual odometry (VO) is a prevalent way to deal with the relative localization problem, which is becoming increasingly mature and accurate, but it tends to be fragile under challenging environments. Comparing with classical geometry-based…
Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information…
In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the…
Training deep neural networks (DNNs) used in modern machine learning is computationally expensive. Machine learning scientists, therefore, rely on stochastic first-order methods for training, coupled with significant hand-tuning, to obtain…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…
Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization have been proposed as memory-efficient alternatives to backpropagation (BP) for gradient computation, especially in low-resource settings. However, their…
Zeroth-order (ZO) optimization with ordinal feedback has emerged as a fundamental problem in modern machine learning systems, particularly in human-in-the-loop settings such as reinforcement learning from human feedback, preference…
We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO). Firstly, for BLO under the assumption that the lower-level functions admit the typical strong convexity assumption, the…
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…
Prompt learning has become a key method for adapting large language models to specific tasks with limited data. However, traditional gradient-based optimization methods for tuning prompts are computationally intensive, posing challenges for…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…