相关论文: "FISTA" in Banach spaces with adaptive discretisat…

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the…

A crucial issue in two-dimensional Nuclear Magnetic Resonance (NMR) is the speed and accuracy of the data inversion. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion…

We present FIESTA, a model selection approach that significantly reduces the computational resources required to reliably identify state-of-the-art performance from large collections of candidate models. Despite being known to produce…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…

In this paper, a novel multiagent based state transition optimization algorithm with linear convergence rate named MASTA is constructed. It first generates an initial population randomly and uniformly. Then, it applies the basic state…

The fine-tuning of pre-trained models has become ubiquitous in generative AI, computer vision, and robotics. Although much attention has been paid to improving the efficiency of fine-tuning model, there has been less scholarship around…

Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and…

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…

Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…

Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…

Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the…

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

The study of multi-task learning has drawn great attention from the community. Despite the remarkable progress, the challenge of optimally learning different tasks simultaneously remains to be explored. Previous works attempt to modify the…

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…

A common approach for performing sparse tensor recovery is to use an N-mode FISTA method. However, this approach may fail in some cases by missing some values in the true support of the tensor and compensating by erroneously assigning…