{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T18:18:00Z","timestamp":1774117080277,"version":"3.50.1"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030676698","type":"print"},{"value":"9783030676704","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-67670-4_8","type":"book-chapter","created":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T17:04:13Z","timestamp":1614186253000},"page":"118-135","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Lagrangian Duality for Constrained Deep Learning"],"prefix":"10.1007","author":[{"given":"Ferdinando","family":"Fioretto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Van Hentenryck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Terrence W. K.","family":"Mak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cuong","family":"Tran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Baldo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michele","family":"Lombardi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,25]]},"reference":[{"key":"8_CR1","unstructured":"Agarwal, A., Beygelzimer, A., Dud\u00edk, M., Langford, J., Wallach, H.: A reductions approach to fair classification. arXiv preprint arXiv:1803.02453 (2018)"},{"key":"8_CR2","doi-asserted-by":"crossref","unstructured":"Aghaei, S., Azizi, M.J., Vayanos, P.: Learning optimal and fair decision trees for non-discriminative decision-making. In: AAAI, pp. 1418\u20131426 (2019)","DOI":"10.1609\/aaai.v33i01.33011418"},{"key":"8_CR3","unstructured":"Amodei, D., et al.: Deep speech 2: end-to-end speech recognition in English and mandarin. In: ICML, pp. 173\u2013182 (2016)"},{"key":"8_CR4","unstructured":"Amos, B., Kolter, J.Z.: Optnet: differentiable optimization as a layer in neural networks. In: ICML, pp. 136\u2013145. JMLR. org (2017)"},{"issue":"1","key":"8_CR5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.4086\/toc.2012.v008a006","volume":"8","author":"S Arora","year":"2012","unstructured":"Arora, S., Hazan, E., Kale, S.: The multiplicative weights update method: a meta-algorithm and applications. Theory Comput. 8(1), 121\u2013164 (2012)","journal-title":"Theory Comput."},{"issue":"1","key":"8_CR6","first-page":"725","volume":"4","author":"ME Baran","year":"1989","unstructured":"Baran, M.E., Wu, F.F.: Optimal capacitor placement on radial distribution systems. IEEE TPD 4(1), 725\u2013734 (1989)","journal-title":"IEEE TPD"},{"key":"8_CR7","doi-asserted-by":"crossref","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J., et al.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations Trends\u00ae Mach. Learn. 3(1), 1\u2013122 (2011)","DOI":"10.1561\/2200000016"},{"issue":"4","key":"8_CR8","doi-asserted-by":"publisher","first-page":"1248","DOI":"10.1109\/59.99376","volume":"5","author":"BH Chowdhury","year":"1990","unstructured":"Chowdhury, B.H., Rahman, S.: A review of recent advances in economic dispatch. IEEE Trans. Power Syst. 5(4), 1248\u20131259 (1990)","journal-title":"IEEE Trans. Power Syst."},{"key":"8_CR9","unstructured":"Coffrin, C., Gordon, D., Scott, P.: NESTA, the NICTA energy system test case archive. CoRR abs\/1411.0359 (2014). http:\/\/arxiv.org\/abs\/1411.0359"},{"key":"8_CR10","doi-asserted-by":"crossref","unstructured":"Collobert, R., Weston, J.: A unified architecture for natural language processing: Deep neural networks with multitask learning. In: ICML, pp. 160\u2013167 (2008)","DOI":"10.1145\/1390156.1390177"},{"key":"8_CR11","unstructured":"Cotter, A., et al.: Training well-generalizing classifiers for fairness metrics and other data-dependent constraints. arXiv preprint arXiv:1807.00028 (2018)"},{"key":"8_CR12","unstructured":"Cotter, A., Gupta, M., Pfeifer, J.: A light touch for heavily constrained SGD. In: Conference on Learning Theory, pp. 729\u2013771 (2016)"},{"key":"8_CR13","unstructured":"Donti, P., Amos, B., Kolter, J.Z.: Task-based end-to-end model learning in stochastic optimization. In: NIPS, pp. 5484\u20135494 (2017)"},{"key":"8_CR14","doi-asserted-by":"crossref","unstructured":"Fioretto, F., Mak, T., Van Hentenryck, P.: Predicting AC optimal power flows: combining deep learning and Lagrangian dual methods. In: AAAI, p. 630 (2020)","DOI":"10.1609\/aaai.v34i01.5403"},{"key":"8_CR15","unstructured":"Fioretto, F., Mak, T.W.K., Baldo, F., Lombardi, M., Van Hentenryck, P.: A lagrangian dual framework for deep neural networks with constraints. CoRR, arXiv:2001.09394 (2020)"},{"issue":"3","key":"8_CR16","doi-asserted-by":"publisher","first-page":"1346","DOI":"10.1109\/TPWRS.2008.922256","volume":"23","author":"EB Fisher","year":"2008","unstructured":"Fisher, E.B., O\u2019Neill, R.P., Ferris, M.C.: Optimal transmission switching. IEEE Trans. Power Syst. 23(3), 1346\u20131355 (2008)","journal-title":"IEEE Trans. Power Syst."},{"key":"8_CR17","doi-asserted-by":"publisher","unstructured":"Fontaine, D., Laurent, M., Van Hentenryck, P.: Constraint-based Lagrangian relaxation. In: O\u2019Sullivan, B. (ed.) Principles and Practice of Constraint Programming. CP 2014. LNCS, vol. 8656, pp. 324\u2013339. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-10428-7_25","DOI":"10.1007\/978-3-319-10428-7_25"},{"key":"8_CR18","unstructured":"Hardt, M., Price, E., Price, E., Srebro, N.: Equality of opportunity in supervised learning. In: Lee, D.D., Sugiyama, M., Luxburg, U.V., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems, vol. 29, pp. 3315\u20133323 (2016)"},{"issue":"7","key":"8_CR19","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1002\/mma.1197","volume":"33","author":"M Herty","year":"2010","unstructured":"Herty, M., Mohring, J., Sachers, V.: A new model for gas flow in pipe networks. Math. Methods Appl. Sci. 33(7), 845\u2013855 (2010)","journal-title":"Math. Methods Appl. Sci."},{"issue":"5","key":"8_CR20","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF0092767","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4(5), 303\u2013320 (1969). https:\/\/doi.org\/10.1007\/BF0092767","journal-title":"J. Optim. Theory Appl."},{"key":"8_CR21","unstructured":"Kearns, M., Neel, S., Roth, A., Wu, Z.S.: Preventing fairness gerrymandering: auditing and learning for subgroup fairness. arXiv preprint arXiv:1711.05144 (2017)"},{"key":"8_CR22","unstructured":"Khalil, E., Dai, H., Zhang, Y., Dilkina, B., Song, L.: Learning combinatorial optimization algorithms over graphs. In: NIPS, pp. 6348\u20136358 (2017)"},{"key":"8_CR23","first-page":"202","volume":"96","author":"R Kohavi","year":"1996","unstructured":"Kohavi, R.: Scaling up the accuracy of Naive-Bayes classifiers: a decision-tree hybrid. KDD 96, 202\u2013207 (1996)","journal-title":"KDD"},{"key":"8_CR24","unstructured":"Kool, W., Van Hoof, H., Welling, M.: Attention, learn to solve routing problems! arXiv preprint arXiv:1803.08475 (2018)"},{"key":"8_CR25","unstructured":"Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: NIPS, pp. 1097\u20131105 (2012)"},{"issue":"1","key":"8_CR26","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1287\/ijoc.2018.0821","volume":"31","author":"TWK Mak","year":"2019","unstructured":"Mak, T.W.K., Hentenryck, P.V., Zlotnik, A., Bent, R.: Dynamic compressor optimization in natural gas pipeline systems. INFORMS J. Comput. 31(1), 40\u201365 (2019)","journal-title":"INFORMS J. Comput."},{"key":"8_CR27","doi-asserted-by":"crossref","unstructured":"Malossi, A.C.I., Schaffner, M., et al.: The transprecision computing paradigm: concept, design, and applications. In: Design, Automation & Test in Europe Conference & Exhibition (DATE), 2018, pp. 1105\u20131110. IEEE (2018)","DOI":"10.23919\/DATE.2018.8342176"},{"issue":"1","key":"8_CR28","first-page":"175","volume":"2","author":"A Monticelli","year":"1987","unstructured":"Monticelli, A., Pereira, M., Granville, S.: Security-constrained optimal power flow with post-contingency corrective rescheduling. IEEE TPS 2(1), 175\u2013180 (1987)","journal-title":"IEEE TPS"},{"key":"8_CR29","unstructured":"Nandwani, Y., Pathak, A., Singla, P.M.: A primal dual formulation for deep learning with constraints. In: NIPS (2019)"},{"key":"8_CR30","unstructured":"Narasimhan, H.: Learning with complex loss functions and constraints. In: International Conference on Artificial Intelligence and Statistics, pp. 1646\u20131654 (2018)"},{"key":"8_CR31","doi-asserted-by":"crossref","unstructured":"Verma, S.N., Mukherjee, V.: Transmission expansion planning: a review. In: International Conference on Energy Efficient Technologies for Sustainability, pp. 350\u2013355 (2016)","DOI":"10.1109\/ICEETS.2016.7583779"},{"key":"8_CR32","doi-asserted-by":"crossref","unstructured":"Parikh, N., Boyd, S., et al.: Proximal algorithms. Foundations Trends\u00ae Optim. 1(3), 127\u2013239 (2014)","DOI":"10.1561\/2400000003"},{"issue":"1","key":"8_CR33","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1080\/10556788.2014.888426","volume":"30","author":"M Pfetsch","year":"2015","unstructured":"Pfetsch, M., et al.: Validation of nominations in gas network optimization: models, methods, and solutions. Optim. Methods Softw. 30(1), 15\u201353 (2015)","journal-title":"Optim. Methods Softw."},{"key":"8_CR34","unstructured":"Vinyals, O., Fortunato, M., Jaitly, N.: Pointer networks. In: NIPS, pp. 2692\u20132700 (2015)"},{"key":"8_CR35","doi-asserted-by":"crossref","unstructured":"Wilder, B., Dilkina, B., Tambe, M.: Melding the data-decisions pipeline: decision-focused learning for combinatorial optimization. In: AAAI, vol. 33, pp. 658\u20131665 (2019)","DOI":"10.1609\/aaai.v33i01.33011658"},{"issue":"2","key":"8_CR36","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1016\/j.eswa.2007.12.020","volume":"36","author":"IC Yeh","year":"2009","unstructured":"Yeh, I.C., Lien, C.H.: The comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clients. Expert Syst. Appl. 36(2), 2473\u20132480 (2009)","journal-title":"Expert Syst. Appl."},{"issue":"75","key":"8_CR37","first-page":"1","volume":"20","author":"MB Zafar","year":"2019","unstructured":"Zafar, M.B., Valera, I., Gomez-Rodriguez, M., Gummadi, K.P.: Fairness constraints: a flexible approach for fair classification. JMLR 20(75), 1\u201342 (2019)","journal-title":"JMLR"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Applied Data Science and Demo Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-67670-4_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,23]],"date-time":"2025-02-23T23:09:34Z","timestamp":1740352174000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-67670-4_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030676698","9783030676704"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-67670-4_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"25 February 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ghent","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Belgium","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 September 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 September 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ecmlpkdd2020.net\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"945","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"195","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"21% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4,5","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4,4","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference took place virtually due to the COVID-19 pandemic","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}