Related papers: Learned Optimizers for Analytic Continuation
This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…
Graph Neural Networks (GNNs) have greatly advanced the semi-supervised node classification task on graphs. The majority of existing GNNs are trained in an end-to-end manner that can be viewed as tackling a bi-level optimization problem.…
We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…
Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is…
We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…
One notable weakness of current machine learning algorithms is the poor ability of models to solve new problems without forgetting previously acquired knowledge. The Continual Learning paradigm has emerged as a protocol to systematically…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…
In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…
For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
Despite the tremendous success of deep neural networks in various learning problems, it has been observed that adding an intentionally designed adversarial perturbation to inputs of these architectures leads to erroneous classification with…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…
Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…