相关论文: Parameter-Free FISTA by Adaptive Restart and Backt…

In this note, we propose a FISTA-type first order algorithm, VAR-FISTA, to solve a composite optimization problem. A distinctive feature of VAR-FISTA is its ability to exploit the convexity of the function in the problem, resulting in an…

It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and…

The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…

The accelerated composite optimization method FISTA (Beck, Teboulle 2009) is suboptimal by a constant factor, and we present a new method OptISTA that improves FISTA by a constant factor of 2. The performance estimation problem (PEP) has…

In this paper, we analyze a speed restarting scheme for the dynamical system given by $$ \ddot{x}(t) + \dfrac{\alpha}{t}\dot{x}(t) + \nabla \phi(x(t)) + \beta \nabla^2 \phi(x(t))\dot{x}(t)=0, $$ where $\alpha$ and $\beta$ are positive…

First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…

In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited.…

Parameter-free stochastic optimization aims to design algorithms that are agnostic to the underlying problem parameters while still achieving convergence rates competitive with optimally tuned methods. While some parameter-free methods do…

Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image…

For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…

Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the…

We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…

We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified decreases in objective values, the specified amounts being the same for all optimization…

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our…

We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…

Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

The optimal learning rate for adaptive gradient methods applied to {\lambda}-strongly convex functions relies on the parameters {\lambda} and learning rate {\eta}. In this paper, we adapt a universal algorithm along the lines of Metagrad,…

Multi-task learning aims to boost the generalization performance of multiple related tasks simultaneously by leveraging information contained in those tasks. In this paper, we propose a multi-task learning framework, where we utilize prior…

We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $\ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters…