{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T23:32:01Z","timestamp":1768347121003,"version":"3.49.0"},"reference-count":31,"publisher":"IEEE","license":[{"start":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T00:00:00Z","timestamp":1734307200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T00:00:00Z","timestamp":1734307200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,16]]},"DOI":"10.1109\/cdc56724.2024.10886398","type":"proceedings-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T18:43:32Z","timestamp":1740595412000},"page":"7846-7852","source":"Crossref","is-referenced-by-count":2,"title":["Remarks on the Gradient Training of Linear Neural Network Based Feedback for the LQR Problem"],"prefix":"10.1109","author":[{"given":"Arthur Castello B.","family":"De Oliveira","sequence":"first","affiliation":[{"name":"Northeastern University,Department of Electrical & Computer Engineering,Boston,MA,USA,02115"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milad","family":"Siami","sequence":"additional","affiliation":[{"name":"Northeastern University,Department of Electrical & Computer Engineering,Boston,MA,USA,02115"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduardo D.","family":"Sontag","sequence":"additional","affiliation":[{"name":"Northeastern University,Department of Electrical & Computer Engineering,Boston,MA,USA,02115"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611977745.4"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.23919\/ACC55779.2023.10155867"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/MLSP55844.2023.10285960"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP48485.2024.10448146"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/LCSYS.2022.3229054"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TAI.2024.3358261"},{"key":"ref7","article-title":"The role of systems theory in control oriented learning","volume-title":"25th International Symposium on Mathematical Theory of Networks and Systems","author":"Sznaier"},{"key":"ref8","article-title":"Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator","author":"Fazel","year":"2019","journal-title":"arXiv:1801.05039 [cs, stat]"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2024.105804"},{"issue":"1","key":"ref10","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TAC.1970.1099363","article-title":"On the determination of the optimal constant output feedback gains for linear multivariable systems","volume":"15","author":"Levine","year":"1970","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"5","key":"ref11","doi-asserted-by":"crossref","first-page":"2435","DOI":"10.1109\/TAC.2021.3087455","article-title":"Convergence and Sample Complexity of Gradient Methods for the Model-Free Linear-Quadratic Regulator Problem","volume":"67","author":"Mohammadi","year":"2022","journal-title":"IEEE Transactions on Automatic Control"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"105138","DOI":"10.1016\/j.sysconle.2022.105138","article-title":"Remarks on input to state stability of perturbed gradient flows, motivated by model-free feedback control learning","volume":"161","author":"Sontag","year":"2022","journal-title":"Systems & Control Letters"},{"key":"ref13","article-title":"Deep Learning without Poor Local Minima","volume":"29","author":"Kawaguchi","year":"2016","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"ref14","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1093\/imaiai\/iaaa039","article-title":"Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers","volume":"11","author":"Bah","year":"2022","journal-title":"Information and Inference: A Journal of the IMA"},{"issue":"1","key":"ref15","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0893-6080(89)90014-2","article-title":"Neural networks and principal component analysis: Learning from examples without local minima","volume":"2","author":"Baldi","year":"1989","journal-title":"Neural Networks"},{"key":"ref16","first-page":"2836","article-title":"Training Linear Neural Networks: Non-Local Convergence and Complexity Results","volume-title":"Proceedings of the 37th International Conference on Machine Learning.","author":"Eftekhari"},{"issue":"3","key":"ref17","doi-asserted-by":"crossref","first-page":"918","DOI":"10.3934\/mcrf.2022021","article-title":"A Geometric Approach of Gradient Descent Algorithms in Linear Neural Networks","volume":"13","author":"Chitour","year":"2023","journal-title":"Mathematical Control and Related Fields"},{"key":"ref18","article-title":"A convergence analysis of gradient descent for deep linear neural networks","author":"Arora","year":"2018","journal-title":"arXiv preprint arXiv:1810.02281"},{"key":"ref19","first-page":"322","article-title":"Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks","volume-title":"International Conference on Machine Learning.","author":"Arora"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/CDC49753.2023.10383478"},{"key":"ref21","first-page":"7760","article-title":"On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks","volume-title":"Proceedings of the 38th International Conference on Machine Learning.","author":"Min"},{"key":"ref22","first-page":"24 850","article-title":"On the convergence of gradient flow on multi-layer linear models","volume-title":"International Conference on Machine Learning.","author":"Min"},{"key":"ref23","first-page":"10153","article-title":"Understanding the Dynamics of Gradient Flow in Overparameterized Linear models","volume-title":"Proceedings of the 38th International Conference on Machine Learning.","author":"Tarmoun"},{"key":"ref24","article-title":"How regularization affects the critical points in linear networks","volume":"30","author":"Taghvaei","year":"2017","journal-title":"Advances in neural information processing systems"},{"key":"ref25","article-title":"Convergence analysis of overparametrized lqr formulations","author":"de Oliveira","year":"2024","journal-title":"arXiv preprint arXiv:2408.15456"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/s1052623495290441"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1907378117"},{"key":"ref28","first-page":"2:1","article-title":"Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions","volume-title":"th Innovations in Theoretical Computer Science Conference (ITCS 2017), ser. Leibniz International Proceedings in Informatics (LIPIcs)","volume":"67","author":"Panageas"},{"key":"ref29","first-page":"1246","article-title":"Gradient descent only converges to minimizers","volume-title":"29th Annual Conference on Learning Theory, ser. Proceedings of Machine Learning Research","volume":"49","author":"Lee"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1947-5"},{"key":"ref31","volume-title":"General Topology, ser. Graduate Texts in Mathematics.","author":"Kelley","year":"1975"}],"event":{"name":"2024 IEEE 63rd Conference on Decision and Control (CDC)","location":"Milan, Italy","start":{"date-parts":[[2024,12,16]]},"end":{"date-parts":[[2024,12,19]]}},"container-title":["2024 IEEE 63rd Conference on Decision and Control (CDC)"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/10885784\/10885785\/10886398.pdf?arnumber=10886398","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T07:33:50Z","timestamp":1740641630000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10886398\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,16]]},"references-count":31,"URL":"https:\/\/doi.org\/10.1109\/cdc56724.2024.10886398","relation":{},"subject":[],"published":{"date-parts":[[2024,12,16]]}}}