{"title":"Predict globally, correct locally: Parallel-in-time optimization of neural networks","authors":"Panos Parpas, Corey Muir","doi":"10.1016/j.automatica.2024.111976","DOIUrl":null,"url":null,"abstract":"<div><div>The training of neural networks can be formulated as an optimal control problem of a dynamical system. The initial conditions of the dynamical system are given by the data. The objective of the control problem is to transform the initial conditions in a form that can be easily classified or regressed using linear methods. This link between optimal control of dynamical systems and neural networks has proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited this link to investigate the stability of different neural network architectures and develop memory efficient training algorithms. In this paper, we also adopt the dynamical systems view of neural networks, but our aim is different from earlier works. Instead, we develop a novel distributed optimization algorithm. The proposed algorithm addresses the most significant obstacle for distributed algorithms for neural network optimization: the network weights cannot be updated until the forward propagation of the data, and backward propagation of the gradients are complete. Using the dynamical systems point of view, we interpret the layers of a (residual) neural network as the discretized dynamics of a dynamical system and exploit the relationship between the co-states (adjoints) of the optimal control problem and backpropagation. We then develop a parallel-in-time method that updates the parameters of the network without waiting for the forward or back propagation algorithms to complete in full. We establish the convergence of the proposed algorithm. Preliminary numerical results suggest that the algorithm is competitive and more efficient than the state-of-the-art.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824004709","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The training of neural networks can be formulated as an optimal control problem of a dynamical system. The initial conditions of the dynamical system are given by the data. The objective of the control problem is to transform the initial conditions in a form that can be easily classified or regressed using linear methods. This link between optimal control of dynamical systems and neural networks has proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited this link to investigate the stability of different neural network architectures and develop memory efficient training algorithms. In this paper, we also adopt the dynamical systems view of neural networks, but our aim is different from earlier works. Instead, we develop a novel distributed optimization algorithm. The proposed algorithm addresses the most significant obstacle for distributed algorithms for neural network optimization: the network weights cannot be updated until the forward propagation of the data, and backward propagation of the gradients are complete. Using the dynamical systems point of view, we interpret the layers of a (residual) neural network as the discretized dynamics of a dynamical system and exploit the relationship between the co-states (adjoints) of the optimal control problem and backpropagation. We then develop a parallel-in-time method that updates the parameters of the network without waiting for the forward or back propagation algorithms to complete in full. We establish the convergence of the proposed algorithm. Preliminary numerical results suggest that the algorithm is competitive and more efficient than the state-of-the-art.
期刊介绍:
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.