{"type":"ScholarlyArticle","title":"Bridging the Gap between General and Down-Closed Convex Sets in Submodular Maximization","authors":[{"name":"Loay Mualem","slug":"loay-mualem","given":"Loay","family":"Mualem","affiliation":"University of Haifa"},{"name":"Murad Tukan","slug":"murad-tukan","given":"Murad","family":"Tukan","affiliation":"DataHeroes"},{"name":"Moran Feldman","slug":"moran-feldman","given":"Moran","family":"Feldman","affiliation":"University of Haifa"}],"abstract":"Optimization of DR-submodular functions has experienced a notable surge in significance in recent times, marking a pivotal development within the domain of non-convex optimization. Motivated by real-world scenarios, some recent works have delved into the maximization of non-monotone DR-submodular functions over general (not necessarily down-closed) convex set constraints. Up to this point, these works have all used the minimum L-infinity norm of any feasible solution as a parameter. Unfortunately, a recent hardness result due to Mualem and Feldman shows that this approach cannot yield a smooth interpolation between down-closed and non-down-closed constraints. In this work, we suggest novel offline and online algorithms that provably provide such an interpolation based on a natural decomposition of the convex body constraint into two distinct convex bodies: a down-closed convex body and a general convex body. We also empirically demonstrate the superiority of our proposed algorithms across three offline and two online applications.","doi":"10.24963/ijcai.2024/213","url":"https://ijcai.org/proceedings/2024/213","pdf":"https://ijcai.org/proceedings/2024/0213.pdf","markdown":"https://ijcai.org/proceedings/2024/213.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/213","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":213,"pages":{"first":1926,"last":1934},"keywords":["Search: S: Combinatorial search and optimisation","Constraint Satisfaction and Optimization: CSO: Constraint optimization problems","Machine Learning: ML: Online learning"],"videos":[],"references":[{"position":1,"raw":"[Abernethy et al., 2008] Jacob Abernethy, Elad Hazan, and Alexander Rakhlin. Competing in the dark: An efficient algorithm for bandit linear optimization. In Conference on Learning Theory (COLT), pages 263-273, 2008.","title":"Competing in the dark: An efficient algorithm for bandit linear optimization","authors":"Abernethy","year":"2008","venue":"Conference on Learning Theory (COLT)","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bian et al., 2017a] An Bian, Kfir Yehuda Levy, Andreas Krause, and Joachim M. Buhmann. Non-monotone con- tinuous DR-submodular maximization: Structure and al- gorithms. In Advances in Neural Information Processing Systems (NeurIPS), pages 486-496, 2017.","title":"Non-monotone continuous DR-submodular maximization: Structure and algorithms","authors":"Bian","year":"2017","venue":"Advances in Neural Information Processing Systems (NeurIPS)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bian et al., 2017b] Andrew An Bian, Baharan Mirza- soleiman, Joachim M. Buhmann, and Andreas Krause. Guaranteed non-convex optimization: Submodular maxi- mization over continuous domains. In Aarti Singh and Xi- aojin (Jerry) Zhu, editors, International Conference on Ar- tificial Intelligence and Statistics (AISTATS), volume 54 of Proceedings of Machine Learning Research, pages 111- 120. PMLR, 2017.","title":"Guaranteed non-convex optimization: Submodular maximization over continuous domains","authors":"Bian","year":"2017","venue":"International Conference on Artificial Intelligence and Statistics (AISTATS)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bian et al., 2019] Yatao Bian, Joachim Buhmann, and An- dreas Krause. Optimal continuous DR-submodular max- imization and applications to provable mean field infer- ence. In International Conference on Machine Learning (ICML), pages 644-653. PMLR, 2019.","title":"Optimal continuous DR-submodular maximization and applications to provable mean field inference","authors":"Bian","year":"2019","venue":"International Conference on Machine Learning (ICML)","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Buchbinder and Feldman, 2023] Niv Buchbinder and Moran Feldman. Constrained submodular maximization via new bounds for dr-submodular functions. CoRR, abs/2311.01129, 2023.","title":"Constrained submodular maximization via new bounds for dr-submodular functions","authors":"Feldman Buchbinder, Niv Buchbinder, Moran Feldman","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Calinescu et al., 2011] Gruia Calinescu, Chandra Chekuri, Martin Pal, and Jan Vondrák. Maximizing a monotone submodular function subject to a matroid constraint. SIAM Journal on Computing, 40(6):1740-1766, 2011.","title":"Maximizing a monotone submodular function subject to a matroid constraint","authors":"Gruia Calinescu, Chandra Chekuri, Martin Pal, Jan Vondrák","year":"2011","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cesa-Bianchi et al., 2007] Nicolò Cesa-Bianchi, Yishay Mansour, and Gilles Stoltz. Improved second-order bounds for prediction with expert advice. Mach. Learn., 66(2-3):321-352, 2007.","title":"Improved second-order bounds for prediction with expert advice","authors":"Nicolò Cesa-Bianchi, Yishay Mansour, Gilles Stoltz","year":"2007","venue":"Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chen et al., 2018] Lin Chen, Hamed Hassani, and Amin Karbasi. Online continuous submodular maximization. In International Conference on Artificial Intelligence and Statistics (AISTATS), pages 1896-1905. PMLR, 2018.","title":"Online continuous submodular maximization","authors":"Lin Chen, Hamed Hassani, Amin Karbasi","year":"2018","venue":"International Conference on Artificial Intelligence and Statistics (AISTATS)","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chen et al., 2019] Lin Chen, Mingrui Zhang, and Amin Karbasi. Projection-free bandit convex optimization. In Kamalika Chaudhuri and Masashi Sugiyama, editors, International Conference on Artificial Intelligence and Statistics (AISTATS), volume 89 of Proceedings of Ma- chine Learning Research, pages 2047-2056. PMLR, 2019.","title":"Projection-free bandit convex optimization","authors":"Lin Chen, Mingrui Zhang, Amin Karbasi","year":"2019","venue":"International Conference on Artificial Intelligence and Statistics (AISTATS)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Du et al., 2022] Donglei Du, Zhicheng Liu, Chenchen Wu, Dachuan Xu, and Yang Zhou. An improved approximation algorithm for maximizing a DR-submodular function over a convex set. arXiv preprint arXiv:2203.14740, 2022.","title":"An improved approximation algorithm for maximizing a DR-submodular function over a convex set","authors":"Du","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Du, 2022] Donglei Du. Lyapunov function approach for approximation algorithm design and analysis: with applications in submodular maximization. CoRR, abs/2205.12442, 2022.","title":"Donglei Du. Lyapunov function approach for approximation algorithm design and analysis: with applications in submodular maximization","authors":"Du","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Dürr et al., 2021] Christoph Dürr, Nguyên Kim Thång, Ab- hinav Srivastav, and Léo Tible. Non-monotone DR- submodular maximization over general convex sets. In In- ternational Joint Conference on Artificial Intelligence (IJ- CAI), pages 2148-2154, 2021.","title":"Non-monotone DRsubmodular maximization over general convex sets","authors":"Christoph Dürr, Nguyên Kim Thång, Abhinav Srivastav, Léo Tible","year":"2021","venue":"ternational Joint Conference on Artificial Intelligence (IJ-CAI)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[El Halabi et al., 2023] Marwa El Halabi, Federico Fusco, Ashkan Norouzi-Fard, Jakab Tardos, and Jakub Tar- nawski. Fairness in streaming submodular maximization over a matroid constraint. In International Conference on Machine Learning, pages 9150-9171. PMLR, 2023.","title":"Fairness in streaming submodular maximization over a matroid constraint","authors":"Marwa El Halabi, Federico Fusco, Ashkan Norouzi-Fard, Jakab Tardos, Jakub Tarnawski","year":"2023","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ene and Nguyen, 2016] Alina Ene and Huy L. Nguyen. Constrained submodular maximization: Beyond 1/e. In Irit Dinur, editor, IEEE 57th Annual Symposium on Foun- dations of Computer Science, FOCS 2016, 9-11 October 2016, Hyatt Regency, New Brunswick, New Jersey, USA, pages 248-257. IEEE Computer Society, 2016.","title":"Constrained submodular maximization: Beyond 1/e","authors":"Alina Ene, L Huy, Nguyen","year":"2016","venue":"IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Feige et al., 2011] Uriel Feige, Vahab S. Mirrokni, and Jan Vondrák. Maximizing non-monotone submodular func- tions. SIAM J. Comput., 40(4):1133-1153, 2011.","title":"Maximizing non-monotone submodular functions","authors":"Uriel Feige, S Vahab, Jan Mirrokni, Vondrák","year":"2011","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Feldman et al., 2011] Moran Feldman, Joseph Naor, and Roy Schwartz. A unified continuous greedy algorithm for submodular maximization. In Foundations of Computer Science (FOCS), pages 570-579, 2011.","title":"A unified continuous greedy algorithm for submodular maximization","authors":"Moran Feldman, Joseph Naor, Roy Schwartz","year":"2011","venue":"Foundations of Computer Science (FOCS)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Feldman, 2021] Moran Feldman. Guess free maximization of submodular and linear sums. Algorithmica, 83(3):853- 878, 2021.","title":"Guess free maximization of submodular and linear sums","authors":"Moran Feldman","year":"2021","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Halabi et al., 2023] Marwa El Halabi, Jakub Tarnawski, Ashkan Norouzi-Fard, and Thuy-Duong Vuong. Fairness in submodular maximization over a matroid constraint. arXiv preprint arXiv:2312.14299, 2023.","title":"Fairness in submodular maximization over a matroid constraint","authors":"Marwa El Halabi, Jakub Tarnawski, Ashkan Norouzi-Fard, Thuy-Duong Vuong","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Hassani et al., 2017] Hamed Hassani, Mahdi Soltanolkotabi, and Amin Karbasi. Gradient meth- ods for submodular maximization. Advances in Neural Information Processing Systems (NeurIPS), 30, 2017.","title":"Gradient methods for submodular maximization","authors":"Hamed Hassani, Mahdi Soltanolkotabi, Amin Karbasi","year":"2017","venue":"Advances in Neural Information Processing Systems (NeurIPS)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Massa et al., 2009] Paolo Massa, Martino Salvetti, and Danilo Tomasoni. Bowling alone and trust decline in so- cial network sites. In IEEE International Conference on Dependable, Autonomic and Secure Computing (DASC), pages 658-663. IEEE Computer Society, 2009.","title":"Bowling alone and trust decline in social network sites","authors":"Paolo Massa, Martino Salvetti, Danilo Tomasoni","year":"2009","venue":"IEEE International Conference on Dependable, Autonomic and Secure Computing (DASC)","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Mitra et al., 2021] Siddharth Mitra, Moran Feldman, and Amin Karbasi. Submodular + concave. In Marc'Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Advances in Neural Information Processing Systems (NeurIPS), pages 11577-11591, 2021.","title":"Submodular + concave","authors":"Siddharth Mitra, Moran Feldman, Amin Karbasi","year":"2021","venue":"Advances in Neural Information Processing Systems (NeurIPS)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Mualem and Feldman, 2022] Loay Mualem and Moran Feldman. Using partial monotonicity in submodular max- imization. In Advances in Neural Information Processing Systems (NeurIPS), 2022.","title":"Using partial monotonicity in submodular maximization","authors":"Feldman Mualem, Loay Mualem, Moran Feldman","year":"2022","venue":"Advances in Neural Information Processing Systems (NeurIPS)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Mualem and Feldman, 2023] Loay Mualem and Moran Feldman. Resolving the approximability of offline and online non-monotone DR-submodular maximization over general convex sets. In Francisco J. R. Ruiz, Jennifer G. Dy, and Jan-Willem van de Meent, editors, International Conference on Artificial Intelligence and Statistics (AIS- TATS), volume 206 of Proceedings of Machine Learning Research, pages 2542-2564. PMLR, 2023.","title":"Resolving the approximability of offline and online non-monotone DR-submodular maximization over general convex sets","authors":"Feldman Mualem, Loay Mualem, Moran Feldman","year":"2023","venue":"International Conference on Artificial Intelligence and Statistics (AIS-TATS)","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Mualem et al., 2023] Loay Mualem, Ethan R Elenberg, Moran Feldman, and Amin Karbasi. Submodular mini- max optimization: Finding effective sets. arXiv preprint arXiv:2305.16903, 2023.","title":"Submodular minimax optimization: Finding effective sets","authors":"Mualem","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Mualem et al., 2024] Loay Mualem, Murad Tukan, and Moran Fledman. Bridging the gap between general and down-closed convex sets in submodular maximization. arXiv preprint arXiv:2401.09251, 2024.","title":"Bridging the gap between general and down-closed convex sets in submodular maximization","authors":"Mualem","year":"2024","venue":null,"doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Nemhauser and Wolsey, 1978] G. L. Nemhauser and L. A. Wolsey. Best algorithms for approximating the maximum of a submodular set function. Math. Oper. Res., 3(3):177- 188, 1978.","title":"Best algorithms for approximating the maximum of a submodular set function","authors":"G L Nemhauser, L A Wolsey","year":"1978","venue":"Math. Oper. Res","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Niazadeh et al., 2020] Rad Niazadeh, Tim Roughgarden, and Joshua R Wang. Optimal algorithms for con- tinuous non-monotone submodular and DR-submodular maximization. Journal of Machine Learning Research, 21(1):4937-4967, 2020.","title":"Optimal algorithms for continuous non-monotone submodular and DR-submodular maximization","authors":"Rad Niazadeh, Tim Roughgarden, Joshua R Wang","year":"2020","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Pedramfar et al., 2023] Mohammad Pedramfar, Christo- pher John Quinn, and Vaneet Aggarwal. A unified ap- proach for maximizing continuous DR-submodular func- tions. arXiv preprint arXiv:2305.16671, 2023.","title":"A unified approach for maximizing continuous DR-submodular functions","authors":"Mohammad Pedramfar, Christopher John Quinn, Vaneet Aggarwal","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Salehi et al., 2017] Mehraveh Salehi, Amin Karbasi, Dustin Scheinost, and R. Todd Constable. A submodular ap- proach to create individualized parcellations of the hu- man brain. In Maxime Descoteaux, Lena Maier-Hein, Alfred M. Franz, Pierre Jannin, D. Louis Collins, and Si- mon Duchesne, editors, International Conference on Med- ical Image Computing and Computer Assisted Interven- tion (MICCAI), volume 10433 of Lecture Notes in Com- puter Science, pages 478-485. Springer, 2017.","title":"A submodular approach to create individualized parcellations of the human brain","authors":"Salehi","year":"2017","venue":"International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI)","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Shi et al., 2021] Guangyao Shi, Ishat E Rabban, Lifeng Zhou, and Pratap Tokekar. Communication-aware multi- robot coordination with submodular maximization. In 2021 IEEE International Conference on Robotics and Au- tomation (ICRA), pages 8955-8961. IEEE, 2021.","title":"Communication-aware multirobot coordination with submodular maximization","authors":"Guangyao Shi, Lifeng Ishat E Rabban, Pratap Zhou, Tokekar","year":"2021","venue":"2021 IEEE International Conference on Robotics and Automation (ICRA)","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Soma and Yoshida, 2017] Tasuku Soma and Yuichi Yoshida. Non-monotone DR-submodular function max- imization. In Satinder Singh and Shaul Markovitch, editors, AAAI Conference on Artificial Intelligence, pages 898-904. AAAI Press, 2017.","title":"Non-monotone DR-submodular function maximization","authors":"Yoshida Soma, Tasuku Soma, Yuichi Yoshida","year":"2017","venue":"AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Th áng and Srivastav, 2021] Nguy ẽn Kim Th áng and Ab- hinav Srivastav. Online non-monotone DR-submodular maximization. In AAAI Conference on Artificial Intelli- gence (AAAI), pages 9868-9876. AAAI Press, 2021.","title":"Nguy ẽn Kim Th áng and Abhinav Srivastav. Online non-monotone DR-submodular maximization","authors":"Th Áng, Srivastav","year":"2021","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Tukan et al., 2023] Murad Tukan, Fares Fares, Yotam Grufinkle, Ido Talmor, Loay Mualem, Vladimir Braver- man, and Dan Feldman. Orbslam3-enhanced autonomous toy drones: Pioneering indoor exploration. arXiv preprint arXiv:2312.13385, 2023.","title":"Orbslam3-enhanced autonomous toy drones: Pioneering indoor exploration","authors":"Murad Tukan, Fares Fares, Yotam Grufinkle, Ido Talmor, Loay Mualem, Vladimir Braverman, Dan Feldman","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Viswanath et al., 2009] Bimal Viswanath, Alan Mislove, Meeyoung Cha, and Krishna P. Gummadi. On the evo- lution of user interaction in facebook. In ACM SIGCOMM Workshop on Social Networks (WOSN), August 2009.","title":"On the evolution of user interaction in facebook","authors":"Bimal Viswanath, Alan Mislove, Meeyoung Cha, Krishna P Gummadi","year":"2009","venue":"ACM SIGCOMM Workshop on Social Networks (WOSN)","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Vondrák, 2013] Jan Vondrák. Symmetry and approximabil- ity of submodular maximization problems. SIAM J. Com- put., 42(1):265-304, 2013.","title":"Jan Vondrák. Symmetry and approximability of submodular maximization problems","authors":"Vondrák","year":"2013","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Yuan and Tang, 2023] Jing Yuan and Shaojie Tang. Group fairness in non-monotone submodular maximization. J. Comb. Optim., 45(3):88, 2023.","title":"Group fairness in non-monotone submodular maximization","authors":"Jing Yuan, Shaojie Tang","year":"2023","venue":"J. Comb. Optim","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Zhang et al., 2019] Mingrui Zhang, Lin Chen, Hamed Has- sani, and Amin Karbasi. Online continuous submodular maximization: From full-information to bandit feedback. In Advances in Neural Information Processing Systems (NeurIPS), volume 32, 2019.","title":"Online continuous submodular maximization: From full-information to bandit feedback","authors":"Zhang","year":"2019","venue":"Advances in Neural Information Processing Systems (NeurIPS)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}