{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T11:37:19Z","timestamp":1777981039029,"version":"3.51.4"},"reference-count":136,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T00:00:00Z","timestamp":1690329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62171038"],"award-info":[{"award-number":["62171038"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62088101"],"award-info":[{"award-number":["62088101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100021130","name":"Bundesministerium f\u00fcr Wirtschaft und Klimaschutz","doi-asserted-by":"crossref","award":["03EI1027"],"award-info":[{"award-number":["03EI1027"]}],"id":[{"id":"10.13039\/100021130","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NSF CAREER Award","award":["2047359"],"award-info":[{"award-number":["2047359"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>Tasks across diverse application domains can be posed as large-scale optimization problems, these include graphics, vision, machine learning, imaging, health, scheduling, planning, and energy system forecasting. Independently of the application domain, proximal algorithms have emerged as a formal optimization method that successfully solves a wide array of existing problems, often exploiting problem-specific structures in the optimization. Although model-based formal optimization provides a principled approach to problem modeling with convergence guarantees, at first glance, this seems to be at odds with black-box deep learning methods. A recent line of work shows that, when combined with learning-based ingredients, model-based optimization methods are effective, interpretable, and allow for generalization to a wide spectrum of applications with little or no extra training data. However, experimenting with such hybrid approaches for different tasks by hand requires domain expertise in both proximal optimization and deep learning, which is often error-prone and time-consuming. Moreover, naively unrolling these iterative methods produces lengthy compute graphs, which when differentiated via autograd techniques results in exploding memory consumption, making batch-based training challenging. In this work, we introduce \u2207-Prox, a domain-specific modeling language and compiler for large-scale optimization problems using differentiable proximal algorithms. \u2207-Prox allows users to specify optimization objective functions of unknowns concisely at a high level, and intelligently compiles the problem into compute and memory-efficient differentiable solvers. One of the core features of \u2207-Prox is its full differentiability, which supports hybrid model- and learning-based solvers integrating proximal optimization with neural network pipelines. Example applications of this methodology include learning-based priors and\/or sample-dependent inner-loop optimization schedulers, learned with deep equilibrium learning or deep reinforcement learning. With a few lines of code, we show \u2207-Prox can generate performant solvers for a range of image optimization problems, including end-to-end computational optics, image deraining, and compressive magnetic resonance imaging. We also demonstrate \u2207-Prox can be used in a completely orthogonal application domain of energy system planning, an essential task in the energy crisis and the clean energy transition, where it outperforms state-of-the-art CVXPY and commercial Gurobi solvers.<\/jats:p>","DOI":"10.1145\/3592144","type":"journal-article","created":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T14:29:21Z","timestamp":1690381761000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["\u2207-Prox: Differentiable Proximal Algorithm Modeling for Large-Scale Optimization"],"prefix":"10.1145","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6102-4916","authenticated-orcid":false,"given":"Zeqiang","family":"Lai","sequence":"first","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9887-0455","authenticated-orcid":false,"given":"Kaixuan","family":"Wei","sequence":"additional","affiliation":[{"name":"McGill University, Montreal, Canada"},{"name":"Princeton University, New Jersey, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6677-694X","authenticated-orcid":false,"given":"Ying","family":"Fu","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9706-1007","authenticated-orcid":false,"given":"Philipp","family":"H\u00e4rtel","sequence":"additional","affiliation":[{"name":"Fraunhofer IEE, Kassel, Germany"},{"name":"Princeton University, New Jersey, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8054-9823","authenticated-orcid":false,"given":"Felix","family":"Heide","sequence":"additional","affiliation":[{"name":"Princeton University, New Jersey, United States"}]}],"member":"320","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2018.0857"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322967"},{"key":"e_1_2_2_3_1","volume-title":"Differentiable convex optimization layers. Advances in neural information processing systems 32","author":"Agrawal Akshay","year":"2019","unstructured":"Akshay Agrawal, Brandon Amos, Shane Barratt, Stephen Boyd, Steven Diamond, and J Zico Kolter. 2019a. Differentiable convex optimization layers. Advances in neural information processing systems 32 (2019)."},{"key":"e_1_2_2_4_1","volume-title":"Differentiating through a cone program. arXiv preprint arXiv:1904.09043","author":"Agrawal Akshay","year":"2019","unstructured":"Akshay Agrawal, Shane Barratt, Stephen Boyd, Enzo Busseti, and Walaa M Moursi. 2019b. Differentiating through a cone program. arXiv preprint arXiv:1904.09043 (2019)."},{"key":"e_1_2_2_5_1","volume-title":"Thomas Nordahl Petersen, Ole Winther, S\u00f8ren Brunak, Gunnar von Heijne, and Henrik Nielsen.","author":"Almagro Armenteros Jos\u00e9 Juan","year":"2019","unstructured":"Jos\u00e9 Juan Almagro Armenteros, Konstantinos D Tsirigos, Casper Kaae S\u00f8nderby, Thomas Nordahl Petersen, Ole Winther, S\u00f8ren Brunak, Gunnar von Heijne, and Henrik Nielsen. 2019. SignalP 5.0 improves signal peptide predictions using deep neural networks. Nature biotechnology 37, 4 (2019), 420--423."},{"key":"e_1_2_2_6_1","volume-title":"International Conference on Machine Learning. PMLR, 136--145","author":"Amos Brandon","year":"2017","unstructured":"Brandon Amos and J Zico Kolter. 2017. Optnet: Differentiable optimization as a layer in neural networks. In International Conference on Machine Learning. PMLR, 136--145."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01586000"},{"key":"e_1_2_2_8_1","volume-title":"Learning to learn by gradient descent by gradient descent. Advances in neural information processing systems 29","author":"Andrychowicz Marcin","year":"2016","unstructured":"Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando De Freitas. 2016. Learning to learn by gradient descent by gradient descent. Advances in neural information processing systems 29 (2016)."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0484-9"},{"key":"e_1_2_2_10_1","volume-title":"Deep equilibrium models. Advances in Neural Information Processing Systems 32","author":"Bai Shaojie","year":"2019","unstructured":"Shaojie Bai, J Zico Kolter, and Vladlen Koltun. 2019. Deep equilibrium models. Advances in Neural Information Processing Systems 32 (2019)."},{"key":"e_1_2_2_11_1","first-page":"1","article-title":"Automatic differentiation in machine learning: a survey","volume":"18","author":"Baydin Atilim Gunes","year":"2018","unstructured":"Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind. 2018. Automatic differentiation in machine learning: a survey. Journal of Marchine Learning Research 18 (2018), 1--43.","journal-title":"Journal of Marchine Learning Research"},{"key":"e_1_2_2_12_1","series-title":"SIAM journal on imaging sciences 2, 1","volume-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","author":"Beck Amir","year":"2009","unstructured":"Amir Beck and Marc Teboulle. 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM journal on imaging sciences 2, 1 (2009), 183--202."},{"key":"e_1_2_2_13_1","volume-title":"Templates for convex cone problems with applications to sparse signal recovery. Mathematical programming computation 3, 3","author":"Becker Stephen R","year":"2011","unstructured":"Stephen R Becker, Emmanuel J Cand\u00e8s, and Michael C Grant. 2011. Templates for convex cone problems with applications to sparse signal recovery. Mathematical programming computation 3, 3 (2011), 165--218."},{"key":"e_1_2_2_14_1","volume-title":"IFIP Conference on System Modeling and Optimization. Springer, 117--126","author":"Benning Martin","year":"2015","unstructured":"Martin Benning, Florian Knoll, Carola-Bibiane Sch\u00f6nlieb, and Tuomo Valkonen. 2015. Preconditioned ADMM with nonlinear operator constraint. In IFIP Conference on System Modeling and Optimization. Springer, 117--126."},{"key":"e_1_2_2_15_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2892632","article-title":"Ebb: A DSL for physical simulation on CPUs and GPUs","volume":"35","author":"Bernstein Gilbert Louis","year":"2016","unstructured":"Gilbert Louis Bernstein, Chinmayee Shah, Crystal Lemire, Zachary Devito, Matthew Fisher, Philip Levis, and Pat Hanrahan. 2016. Ebb: A DSL for physical simulation on CPUs and GPUs. ACM Transactions on Graphics (TOG) 35, 2 (2016), 1--12.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_2_16_1","volume-title":"Efficient and modular implicit differentiation. arXiv preprint arXiv:2105.15183","author":"Blondel Mathieu","year":"2021","unstructured":"Mathieu Blondel, Quentin Berthet, Marco Cuturi, Roy Frostig, Stephan Hoyer, Felipe Llinares-L\u00f3pez, Fabian Pedregosa, and Jean-Philippe Vert. 2021. Efficient and modular implicit differentiation. arXiv preprint arXiv:2105.15183 (2021)."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eneco.2021.105709"},{"key":"e_1_2_2_18_1","doi-asserted-by":"crossref","unstructured":"Stephen Boyd Neal Parikh Eric Chu Borja Peleato Jonathan Eckstein et al. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends\u00ae in Machine learning 3 1 (2011) 1--122.","DOI":"10.1561\/2200000016"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1975-13874-2"},{"key":"e_1_2_2_20_1","volume-title":"A non-local algorithm for image denoising. In 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR'05)","author":"Buades Antoni","unstructured":"Antoni Buades, Bartomeu Coll, and J-M Morel. 2005. A non-local algorithm for image denoising. In 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR'05), Vol. 2. Ieee, 60--65."},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291600009X"},{"key":"e_1_2_2_23_1","volume-title":"Learning to optimize: A primer and a benchmark. arXiv preprint arXiv:2103.12828","author":"Chen Tianlong","year":"2021","unstructured":"Tianlong Chen, Xiaohan Chen, Wuyang Chen, Howard Heaton, Jialin Liu, Zhangyang Wang, and Wotao Yin. 2021. Learning to optimize: A primer and a benchmark. arXiv preprint arXiv:2103.12828 (2021)."},{"key":"e_1_2_2_24_1","volume-title":"Training deep nets with sublinear memory cost. arXiv preprint arXiv:1604.06174","author":"Chen Tianqi","year":"2016","unstructured":"Tianqi Chen, Bing Xu, Chiyuan Zhang, and Carlos Guestrin. 2016. Training deep nets with sublinear memory cost. arXiv preprint arXiv:1604.06174 (2016)."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.joule.2022.05.010"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3132188"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.84"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.5555\/2946645.3007036"},{"key":"e_1_2_2_29_1","volume-title":"Unrolled optimization with deep priors. arXiv preprint arXiv:1705.08041","author":"Diamond Steven","year":"2017","unstructured":"Steven Diamond, Vincent Sitzmann, Felix Heide, and Gordon Wetzstein. 2017. Unrolled optimization with deep priors. arXiv preprint arXiv:1705.08041 (2017)."},{"key":"e_1_2_2_30_1","volume-title":"Denoising prior driven deep neural network for image restoration","author":"Dong Weisheng","year":"2018","unstructured":"Weisheng Dong, Peiyao Wang, Wotao Yin, Guangming Shi, Fangfang Wu, and Xiaotong Lu. 2018. Denoising prior driven deep neural network for image restoration. IEEE transactions on pattern analysis and machine intelligence 41, 10 (2018), 2305--2318."},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-016-0647-7"},{"key":"e_1_2_2_32_1","doi-asserted-by":"crossref","unstructured":"Vincent Fran\u00e7ois-Lavet Peter Henderson Riashat Islam Marc G Bellemare Joelle Pineau et al. 2018. An introduction to deep reinforcement learning. Foundations and Trends\u00ae in Machine Learning 11 3--4 (2018) 219--354.","DOI":"10.1561\/2200000071"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/EEM54602.2022.9921154"},{"key":"e_1_2_2_34_1","first-page":"3404","article-title":"Coded hyperspectral image reconstruction using deep external and internal learning","volume":"44","author":"Fu Ying","year":"2022","unstructured":"Ying Fu, Tao Zhang, Lizhi Wang, and Hua Huang. 2022. Coded hyperspectral image reconstruction using deep external and internal learning. IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 7 (2022), 3404--3420.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"e_1_2_2_35_1","volume-title":"A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & mathematics with applications 2, 1","author":"Gabay Daniel","year":"1976","unstructured":"Daniel Gabay and Bertrand Mercier. 1976. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & mathematics with applications 2, 1 (1976), 17--40."},{"key":"e_1_2_2_36_1","volume-title":"Mixed Hierarchy Network for Image Restoration. arXiv preprint arXiv:2302.09554","author":"Gao Hu","year":"2023","unstructured":"Hu Gao and Depeng Dang. 2023. Mixed Hierarchy Network for Image Restoration. arXiv preprint arXiv:2302.09554 (2023)."},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/83.392335"},{"key":"e_1_2_2_38_1","volume-title":"Distributed convex optimization with many convex constraints. arXiv preprint arXiv:1610.02967","author":"Giesen Joachim","year":"2016","unstructured":"Joachim Giesen and S\u00f6ren Laue. 2016. Distributed convex optimization with many convex constraints. arXiv preprint arXiv:1610.02967 (2016)."},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2021.3118944"},{"key":"e_1_2_2_40_1","volume-title":"Deep learning","author":"Goodfellow Ian","unstructured":"Ian Goodfellow, Yoshua Bengio, and Aaron Courville. 2016. Deep learning. MIT press."},{"key":"e_1_2_2_41_1","first-page":"1095","article-title":"Introduction to Fourier optics","volume":"8","author":"Goodman Joseph W","year":"1996","unstructured":"Joseph W Goodman and P Sutton. 1996. Introduction to Fourier optics. Quantum and Semiclassical Optics-Journal of the European Optical Society Part B 8, 5 (1996), 1095.","journal-title":"Quantum and Semiclassical Optics-Journal of the European Optical Society Part B"},{"key":"e_1_2_2_42_1","volume-title":"CVX: Matlab Software for Disciplined Convex Programming, version 2.1","author":"Grant Michael","year":"2014","unstructured":"Michael Grant and Stephen Boyd. 2014. CVX: Matlab Software for Disciplined Convex Programming, version 2.1. http:\/\/cvxr.com\/cvx."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.5555\/3104322.3104374"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-016-0930-5"},{"key":"e_1_2_2_45_1","unstructured":"LLC Gurobi Optimization. 2018. Gurobi optimizer reference manual."},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2018.2849326"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2020.3023474"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eneco.2020.105051"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601174"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925875"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661260"},{"key":"e_1_2_2_53_1","volume-title":"Jonathan Le Roux, and Felix Weninger","author":"Hershey John R","year":"2014","unstructured":"John R Hershey, Jonathan Le Roux, and Felix Weninger. 2014. Deep unfolding: Modelbased inspiration of novel deep architectures. arXiv preprint arXiv:1409.2574 (2014)."},{"key":"e_1_2_2_54_1","volume-title":"Convolutional neural networks that teach microscopes how to image. ArXiv abs\/1709.07223","author":"Horstmeyer Roarke","year":"2017","unstructured":"Roarke Horstmeyer, Richard Y. Chen, Barbara Kappes, and Benjamin Judkewitz. 2017. Convolutional neural networks that teach microscopes how to image. ArXiv abs\/1709.07223 (2017)."},{"key":"e_1_2_2_55_1","volume-title":"Difftaichi: Differentiable programming for physical simulation. arXiv preprint arXiv:1910.00935","author":"Hu Yuanming","year":"2019","unstructured":"Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Fr\u00e9do Durand. 2019a. Difftaichi: Differentiable programming for physical simulation. arXiv preprint arXiv:1910.00935 (2019)."},{"key":"e_1_2_2_56_1","first-page":"1","article-title":"Taichi: a language for high-performance computation on spatially sparse data structures","volume":"38","author":"Hu Yuanming","year":"2019","unstructured":"Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Fr\u00e9do Durand. 2019b. Taichi: a language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG) 38, 6 (2019), 1--16.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7299156"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-017-0130-5"},{"key":"e_1_2_2_59_1","first-page":"21043","article-title":"Accelerating quadratic optimization with reinforcement learning","volume":"34","author":"Ichnowski Jeffrey","year":"2021","unstructured":"Jeffrey Ichnowski, Paras Jain, Bartolomeo Stellato, Goran Banjac, Michael Luo, Francesco Borrelli, Joseph E Gonzalez, Ion Stoica, and Ken Goldberg. 2021. Accelerating quadratic optimization with reinforcement learning. Advances in Neural Information Processing Systems 34 (2021), 21043--21055.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530099"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2022.3199595"},{"key":"e_1_2_2_62_1","volume-title":"Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980","author":"Kingma Diederik P","year":"2014","unstructured":"Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)."},{"key":"e_1_2_2_63_1","doi-asserted-by":"publisher","DOI":"10.1145\/2866569"},{"key":"e_1_2_2_64_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2014.2377273"},{"key":"e_1_2_2_65_1","volume-title":"Deep Plug-and-Play Prior for Hyperspectral Image Restoration. Neurocomputing","author":"Lai Zeqiang","year":"2022","unstructured":"Zeqiang Lai, Kaixuan Wei, and Ying Fu. 2022. Deep Plug-and-Play Prior for Hyperspectral Image Restoration. Neurocomputing (2022)."},{"key":"e_1_2_2_66_1","volume-title":"Deep learning. Nature 521, 7553","author":"LeCun Yann","year":"2015","unstructured":"Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. 2015. Deep learning. Nature 521, 7553 (2015), 436--444."},{"key":"e_1_2_2_67_1","doi-asserted-by":"publisher","DOI":"10.1137\/140998135"},{"key":"e_1_2_2_68_1","volume-title":"Learning to optimize. arXiv preprint arXiv:1606.01885","author":"Li Ke","year":"2016","unstructured":"Ke Li and Jitendra Malik. 2016. Learning to optimize. arXiv preprint arXiv:1606.01885 (2016)."},{"key":"e_1_2_2_69_1","volume-title":"International Conference on Machine Learning. PMLR, 2111--2119","author":"Li Qunwei","year":"2017","unstructured":"Qunwei Li, Yi Zhou, Yingbin Liang, and Pramod K Varshney. 2017. Convergence analysis of proximal gradient with momentum for nonconvex optimization. In International Conference on Machine Learning. PMLR, 2111--2119."},{"key":"e_1_2_2_70_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275055"},{"key":"e_1_2_2_71_1","volume-title":"Principles of magnetic resonance imaging","author":"Liang Zhi-Pei","unstructured":"Zhi-Pei Liang and Paul C Lauterbur. 2000. Principles of magnetic resonance imaging. SPIE Optical Engineering Press Bellingham."},{"key":"e_1_2_2_72_1","volume-title":"Online Deep Equilibrium Learning for Regularization by Denoising. arXiv preprint arXiv:2205.13051","author":"Liu Jiaming","year":"2022","unstructured":"Jiaming Liu, Xiaojian Xu, Weijie Gan, Shirin Shoushtari, and Ulugbek S Kamilov. 2022. Online Deep Equilibrium Learning for Regularization by Denoising. arXiv preprint arXiv:2205.13051 (2022)."},{"key":"e_1_2_2_73_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2914461"},{"key":"e_1_2_2_74_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.911828"},{"key":"e_1_2_2_75_1","doi-asserted-by":"publisher","DOI":"10.1145\/3453986"},{"key":"e_1_2_2_76_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2001.937655"},{"key":"e_1_2_2_77_1","unstructured":"Luke Metz James Harrison C Daniel Freeman Amil Merchant Lucas Beyer James Bradbury Naman Agrawal Ben Poole Igor Mordatch Adam Roberts et al. 2022. VeLO: Training Versatile Learned Optimizers by Scaling Up. arXiv preprint arXiv:2211.09760 (2022)."},{"key":"e_1_2_2_78_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00145"},{"key":"e_1_2_2_79_1","volume-title":"International conference on machine learning. PMLR","author":"Mnih Volodymyr","year":"2016","unstructured":"Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. 2016. Asynchronous methods for deep reinforcement learning. In International conference on machine learning. PMLR, 1928--1937."},{"key":"e_1_2_2_80_1","doi-asserted-by":"publisher","DOI":"10.1137\/140976601"},{"key":"e_1_2_2_81_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2020.3016905"},{"key":"e_1_2_2_82_1","volume-title":"Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien. Bulletin de la Soci\u00e9t\u00e9 math\u00e9matique de France 93","author":"Moreau Jean-Jacques","year":"1965","unstructured":"Jean-Jacques Moreau. 1965. Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien. Bulletin de la Soci\u00e9t\u00e9 math\u00e9matique de France 93 (1965), 273--299."},{"key":"e_1_2_2_83_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.01688"},{"key":"e_1_2_2_84_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925952"},{"key":"e_1_2_2_85_1","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4173442"},{"key":"e_1_2_2_86_1","volume-title":"International Conference on Machine Learning. PMLR, 343--352","author":"Nishihara Robert","year":"2015","unstructured":"Robert Nishihara, Laurent Lessard, Ben Recht, Andrew Packard, and Michael Jordan. 2015. A general analysis of the convergence of ADMM. In International Conference on Machine Learning. PMLR, 343--352."},{"key":"e_1_2_2_87_1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1366307"},{"key":"e_1_2_2_88_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSAIT.2020.2991563"},{"key":"e_1_2_2_89_1","doi-asserted-by":"publisher","DOI":"10.1137\/040605412"},{"key":"e_1_2_2_90_1","volume-title":"Ulas Baran Baloglu, Ozal Yildirim, and U Rajendra Acharya.","author":"Ozturk Tulin","year":"2020","unstructured":"Tulin Ozturk, Muhammed Talo, Eylul Azra Yildirim, Ulas Baran Baloglu, Ozal Yildirim, and U Rajendra Acharya. 2020. Automated detection of COVID-19 cases using deep neural networks with X-ray images. Computers in biology and medicine 121 (2020), 103792."},{"key":"e_1_2_2_91_1","doi-asserted-by":"publisher","DOI":"10.1561\/9781601987174"},{"key":"e_1_2_2_92_1","unstructured":"Adam Paszke Sam Gross Soumith Chintala Gregory Chanan Edward Yang Zachary DeVito Zeming Lin Alban Desmaison Luca Antiga and Adam Lerer. 2017. Automatic differentiation in pytorch. (2017)."},{"key":"e_1_2_2_93_1","volume-title":"Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems 32","author":"Paszke Adam","year":"2019","unstructured":"Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. 2019. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems 32 (2019)."},{"key":"e_1_2_2_94_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356526"},{"key":"e_1_2_2_95_1","volume-title":"Stuart Anderson, et al.","author":"Pineda Luis","year":"2022","unstructured":"Luis Pineda, Taosha Fan, Maurizio Monge, Shobha Venkataraman, Paloma Sodhi, Ricky Chen, Joseph Ortiz, Daniel DeTone, Austin Wang, Stuart Anderson, et al. 2022. Theseus: A library for differentiable nonlinear optimization. arXiv preprint arXiv:2207.09442 (2022)."},{"key":"e_1_2_2_96_1","doi-asserted-by":"publisher","DOI":"10.1145\/2499370.2462176"},{"key":"e_1_2_2_97_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00406"},{"key":"e_1_2_2_98_1","volume-title":"Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Mathematics of operations research 1, 2","author":"Rockafellar R Tyrrell","year":"1976","unstructured":"R Tyrrell Rockafellar. 1976. Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Mathematics of operations research 1, 2 (1976), 97--116."},{"key":"e_1_2_2_99_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"e_1_2_2_100_1","unstructured":"Mark Segal and Kurt Akeley. 1999. The OpenGL graphics system: A specification (version 1.1)."},{"key":"e_1_2_2_101_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530185"},{"key":"e_1_2_2_102_1","volume-title":"Modelbased deep learning. arXiv preprint arXiv:2012.08405","author":"Shlezinger Nir","year":"2020","unstructured":"Nir Shlezinger, Jay Whang, Yonina C Eldar, and Alexandros G Dimakis. 2020. Modelbased deep learning. arXiv preprint arXiv:2012.08405 (2020)."},{"key":"e_1_2_2_103_1","volume-title":"International conference on machine learning. PMLR, 387--395","author":"Silver David","year":"2014","unstructured":"David Silver, Guy Lever, Nicolas Heess, Thomas Degris, Daan Wierstra, and Martin Riedmiller. 2014. Deterministic policy gradient algorithms. In International conference on machine learning. PMLR, 387--395."},{"key":"e_1_2_2_104_1","doi-asserted-by":"crossref","unstructured":"David Silver Julian Schrittwieser Karen Simonyan Ioannis Antonoglou Aja Huang Arthur Guez Thomas Hubert Lucas Baker Matthew Lai Adrian Bolton et al. 2017. Mastering the game of Go without human knowledge. Nature 550 7676 (2017) 354--359.","DOI":"10.1038\/nature24270"},{"key":"e_1_2_2_105_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201333"},{"key":"e_1_2_2_106_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-020-00179-2"},{"key":"e_1_2_2_107_1","unstructured":"Jian Sun Huibin Li Zongben Xu et al. 2016. Deep ADMM-Net for compressive sensing MRI. Advances in neural information processing systems 29 (2016)."},{"key":"e_1_2_2_108_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00146"},{"key":"e_1_2_2_109_1","volume-title":"International conference on machine learning. PMLR, 9229--9248","author":"Sun Yu","year":"2020","unstructured":"Yu Sun, Xiaolong Wang, Zhuang Liu, John Miller, Alexei Efros, and Moritz Hardt. 2020b. Test-time training with self-supervision for generalization under distribution shifts. In International conference on machine learning. PMLR, 9229--9248."},{"key":"e_1_2_2_110_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2020.07.025"},{"key":"e_1_2_2_111_1","doi-asserted-by":"publisher","DOI":"10.1145\/3446791"},{"key":"e_1_2_2_112_1","doi-asserted-by":"publisher","DOI":"10.1109\/HPTCDL.2014.5"},{"key":"e_1_2_2_113_1","doi-asserted-by":"crossref","unstructured":"Robert J Vanderbei et al. 2020. Linear programming. Springer.","DOI":"10.1007\/978-3-030-39415-8"},{"key":"e_1_2_2_114_1","doi-asserted-by":"publisher","DOI":"10.1109\/GlobalSIP.2013.6737048"},{"key":"e_1_2_2_115_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3450626.3459804","article-title":"Path replay backpropagation: differentiating light paths using constant memory and linear time","volume":"40","author":"Vicini Delio","year":"2021","unstructured":"Delio Vicini, S\u00e9bastien Speierer, and Wenzel Jakob. 2021. Path replay backpropagation: differentiating light paths using constant memory and linear time. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1--14.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_2_116_1","doi-asserted-by":"publisher","DOI":"10.1137\/10078356X"},{"key":"e_1_2_2_117_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-018-0757-z"},{"key":"e_1_2_2_118_1","first-page":"1","article-title":"TFPNP: Tuning-free plug-and-play proximal algorithms with applications to inverse imaging problems","volume":"23","author":"Wei Kaixuan","year":"2022","unstructured":"Kaixuan Wei, Angelica Aviles-Rivero, Jingwei Liang, Ying Fu, Hua Huang, and Carola-Bibiane Sch\u00f6nlieb. 2022a. TFPNP: Tuning-free plug-and-play proximal algorithms with applications to inverse imaging problems. Journal of Machine Learning Research 23, 16 (2022), 1--48.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_2_119_1","volume-title":"International Conference on Machine Learning. PMLR, 10158--10169","author":"Wei Kaixuan","year":"2020","unstructured":"Kaixuan Wei, Angelica Aviles-Rivero, Jingwei Liang, Ying Fu, Carola-Bibiane Sch\u00f6nlieb, and Hua Huang. 2020. Tuning-free plug-and-play proximal algorithm for inverse imaging problems. In International Conference on Machine Learning. PMLR, 10158--10169."},{"key":"e_1_2_2_120_1","first-page":"8520","article-title":"Physics-based noise modeling for extreme low-light photography","volume":"44","author":"Wei Kaixuan","year":"2022","unstructured":"Kaixuan Wei, Ying Fu, Yinqiang Zheng, and Jiaolong Yang. 2022b. Physics-based noise modeling for extreme low-light photography. IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 11 (2022), 8520--8537.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"e_1_2_2_121_1","volume-title":"International Conference on Machine Learning. PMLR, 3751--3760","author":"Wichrowska Olga","year":"2017","unstructured":"Olga Wichrowska, Niru Maheswaranathan, Matthew W Hoffman, Sergio Gomez Colmenarejo, Misha Denil, Nando Freitas, and Jascha Sohl-Dickstein. 2017. Learned optimizers that scale and generalize. In International Conference on Machine Learning. PMLR, 3751--3760."},{"key":"e_1_2_2_122_1","first-page":"67","article-title":"Numerical optimization","volume":"35","author":"Wright Stephen","year":"1999","unstructured":"Stephen Wright, Jorge Nocedal, et al. 1999. Numerical optimization. Springer Science 35, 67--68 (1999), 7.","journal-title":"Springer Science"},{"key":"e_1_2_2_123_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.00351"},{"key":"e_1_2_2_124_1","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.3006390"},{"key":"e_1_2_2_125_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2010.2042333"},{"key":"e_1_2_2_126_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.00079"},{"key":"e_1_2_2_127_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.00564"},{"key":"e_1_2_2_128_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01458"},{"key":"e_1_2_2_129_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00196"},{"key":"e_1_2_2_130_1","volume-title":"Luc Van Gool, and Radu Timofte","author":"Zhang Kai","year":"2021","unstructured":"Kai Zhang, Yawei Li, Wangmeng Zuo, Lei Zhang, Luc Van Gool, and Radu Timofte. 2021. Plug-and-play image restoration with deep denoiser prior. IEEE Transactions on Pattern Analysis and Machine Intelligence (2021)."},{"key":"e_1_2_2_131_1","volume-title":"Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising","author":"Zhang Kai","year":"2017","unstructured":"Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang. 2017a. Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE transactions on image processing 26, 7 (2017), 3142--3155."},{"key":"e_1_2_2_132_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.300"},{"key":"e_1_2_2_133_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2018.2839891"},{"key":"e_1_2_2_134_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-022-01660-2"},{"key":"e_1_2_2_135_1","volume-title":"Object detection with deep learning: A review","author":"Zhao Zhong-Qiu","year":"2019","unstructured":"Zhong-Qiu Zhao, Peng Zheng, Shou-tao Xu, and Xindong Wu. 2019. Object detection with deep learning: A review. IEEE transactions on neural networks and learning systems 30, 11 (2019), 3212--3232."},{"key":"e_1_2_2_136_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2011.6126278"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3592144","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3592144","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T16:37:46Z","timestamp":1750178266000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3592144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,26]]},"references-count":136,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1145\/3592144"],"URL":"https:\/\/doi.org\/10.1145\/3592144","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,26]]},"assertion":[{"value":"2023-07-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}