相关论文: Frequency-Domain Representation of First-Order Met…

Multi-objective optimization (MOO) lies at the core of many machine learning (ML) applications that involve multiple, potentially conflicting objectives (e.g., multi-task learning, multi-objective reinforcement learning, among many others).…

First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…

In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…

Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy…

Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization…

One of the challenges for neural networks in real-life applications is the overconfident errors these models make when the data is not from the original training distribution. Addressing this issue is known as Out-of-Distribution (OOD)…

In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…

We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…

Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…

Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…

Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…

In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…

The $L_1$-regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing $L_1$-regularized models, as an improved substitute of…

We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…

We consider distributed optimization over networks where each agent is associated with a smooth and strongly convex local objective function. We assume that the agents only have access to unbiased estimators of the gradient of their…

We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on $\mathcal{M}_k^{m\times n}$ -- the set of $m\times n$ real matrices with a fixed rank $k$. Our analysis is…

The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving…

Pre-trained diffusion models have shown great potential in real-world image super-resolution (Real-ISR) tasks by enabling high-resolution reconstructions. While one-step diffusion (OSD) methods significantly improve efficiency compared to…

The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient…

Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations…