The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-solved optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches.
Vanderbilt University（范德堡大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring near-real-time optimization. The majority of existing approaches focus on learning data-driven optimizers that lead to fewer iterations in solving an optimization. In this paper, we take a different approach and propose to replace the iterative solvers altogether with a trainable parametric set function, that outputs the optimal arguments/parameters of an optimizat…
Technical University of Munich（慕尼黑工业大学）；LTCI, Telecom Paris, IP Paris（巴黎理工学院巴黎电信学院LTCI）；Columbia University（哥伦比亚大学）
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby a…
LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers
School of Computer Science, Huazhong University of Science and Technology, China（华中科技大学计算机学院）；Department of Computer Science, Cornell University, United States（康奈尔大学计算机系）
NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
Leibniz University Hannover（莱布尼茨汉诺威大学）；Institute of Photonics（光子研究所）；Department of Mathematics and Physics（数学与物理系）；Tsinghua University（清华大学）；Institute of Structural Mechanics（结构力学研究所）；Bauhaus-Universität Weimar（魏玛建筑学院）
We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee linear convergence. However, a major difficulty in choosing the sketch size in terms of the effective dimension lies in the fact that the latter is usually unknown in practice. Current sketching-based solvers for regularized least-squares fall short on addressing this issue. Our main contribution is to propose adaptive versions of standard sketching-based iter…
NTT Communication Science Laboratories（NTT通信科学研究所）；NTT Software Innovation Center（NTT软件创新中心）
Neural network-based anomaly detection methods have shown to achieve high performance. However, they require a large amount of training data for each task. We propose a neural network-based meta-learning method for supervised anomaly detection. The proposed method improves the anomaly detection performance on unseen tasks, which contains a few labeled normal and anomalous instances, by meta-training with various datasets. With a meta-learning framework, quick adaptation to each task and its effective backpropagation are important since the model is trained by the adaptation for each epoch. Our…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already attracted major attention from scientists. Despite their powerful approximation capabilities, however, surrogates cannot produce the `exact' solution to the problem. To address this issue, this paper exploits up-to-date ML tools and delivers customized iterative solvers of linear equation systems, capable of solving large-scale parametrized problems at any desired…
INEUS: Iterative Neural Solver for High-Dimensional PIDEs
Department of Mathematics and RiskLab, ETH Zurich（数学系和风险实验室，苏黎世联邦理工学院）；Applied Mathematics: Institute for Analysis and Numerics, University of Münster（应用数学：分析与数值计算研究所，蒙斯特大学）
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for better stability and correctness. The existing implicit schemes are usually iterative and employ a general-purpose solver which may be sub-optimal for a specific class of PDEs. In this paper, we propose a neural solver to learn an optimal iterative scheme for a class of PDEs, in a data-driven fashion. We attain this objective by modifying an iteration of an …
We describe an approach to Grammatical Error Correction (GEC) that is effective at making use of models trained on large amounts of weakly supervised bitext. We train the Transformer sequence-to-sequence model on 4B tokens of Wikipedia revisions and employ an iterative decoding strategy that is tailored to the loosely-supervised nature of the Wikipedia training corpus. Finetuning on the Lang-8 corpus and ensembling yields an F0.5 of 58.3 on the CoNLL'14 benchmark and a GLEU of 62.4 on JFLEG. The combination of weakly supervised training and iterative decoding obtains an F0.5 of 48.2 on CoNLL'1…
Large scale datasets created from user labels or openly available data have become crucial to provide training data for large scale learning algorithms. While these datasets are easier to acquire, the data are frequently noisy and unreliable, which is motivating research on weakly supervised learning techniques. In this paper we propose an iterative learning method that extracts the useful information from a large scale change detection dataset generated from open vector data to train a fully convolutional network which surpasses the performance obtained by naive supervised learning. We also p…
NPSolver: Neural Poisson Solver with Iterative Physics Supervision
Gaoling School of Artificial Intelligence（高岭人工智能学院）；Renmin University of China（中国人民大学）；School of Mechanics and Engineering Science（力学与工程科学学院）；Peking University（北京大学）；AI for Science Institute（AI for Science研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Recent studies have demonstrated the cross-lingual alignment ability of multilingual pretrained language models. In this work, we found that the cross-lingual alignment can be further improved by training seq2seq models on sentence pairs mined using their own encoder outputs. We utilized these findings to develop a new approach -- cross-lingual retrieval for iterative self-supervised training (CRISS), where mining and training processes are applied iteratively, improving cross-lingual alignment and translation ability at the same time. Using this method, we achieved state-of-the-art unsupervis…
Neural networks that are based on unfolding of an iterative solver, such as LISTA (learned iterative soft threshold algorithm), are widely used due to their accelerated performance. Nevertheless, as opposed to non-learned solvers, these networks are trained on a certain dictionary, and therefore they are inapplicable for varying model scenarios. This work introduces an adaptive learned solver, termed Ada-LISTA, which receives pairs of signals and their corresponding dictionaries as inputs, and learns a universal architecture to serve them all. We prove that this scheme is guaranteed to solve s…
Although data is abundant, data labeling is expensive. Semi-supervised learning methods combine a few labeled samples with a large corpus of unlabeled data to effectively train models. This paper introduces our proposed method LiDAM, a semi-supervised learning approach rooted in both domain adaptation and self-paced learning. LiDAM first performs localized domain shifts to extract better domain-invariant features for the model that results in more accurate clusters and pseudo-labels. These pseudo-labels are then aligned with real class labels in a self-paced fashion using a novel iterative mat…
Technical University Munich（慕尼黑工业大学）；École normale supérieure, Paris（巴黎高等师范学院）；deepc GmbH, Munich（慕尼黑deepc有限公司）；Helmholtz Zentrum München（慕尼黑亥姆霍兹研究中心）；University of Zurich（苏黎世大学）
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over explicit ones to improve stability and correctness. However, existing semi-implicit methods are usually iterative and employ a general-purpose solver, which may be sub-optimal for a specific class of PDEs. In this paper, we propose a neural solver to learn an optimal iterative scheme in a data-driven fashion for any class of PDEs. Specifically, we modify a si…
Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching
University of Chicago（芝加哥大学）；University of California, Berkeley（加州大学伯克利分校）；International Computer Science Institute（国际计算机科学研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
In this paper, we consider the problem of $\ell_{p}$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. The problem, even though convex, does not enjoy a closed-form solution. The state-of-the-art algorithms are iterative but suffer from convergence issues, i.e., they either diverge for p>3 or the convergence to the optimal solution is sensitive to the initialization of the algorithm. Also, these algorithms are not generalizable to every possible value of $p$. In this paper, we propose an iterative algorithm : Paral…
Imperial College London（帝国理工学院）；Inria（法国国家信息与自动化研究所）；Univ Rennes（雷恩大学）；CNRS（法国国家科学研究中心）；IRISA（法国雷恩信息与自动化系统研究所）
Few-shot learning amounts to learning representations and acquiring knowledge such that novel tasks may be solved with both supervision and data being limited. Improved performance is possible by transductive inference, where the entire test set is available concurrently, and semi-supervised learning, where more unlabeled data is available. Focusing on these two settings, we introduce a new algorithm that leverages the manifold structure of the labeled and unlabeled data distribution to predict pseudo-labels, while balancing over classes and using the loss value distribution of a limited-capac…
Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but…
