Stochastic submodular maximization: The case of coverage functions

Advances in Neural Information Processing Systems

Volumn 2017-December, Issue , 2017, Pages 6854-6864

  Karimi, Mohammad Reza ^a   Lucic, Mario ^a   Hassani, Hamed ^b   Krause, Andreas ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LEARNING SYSTEMS; OPTIMIZATION; STOCHASTIC SYSTEMS;

CONTINUOUS OPTIMIZATION; INFLUENCE MAXIMIZATIONS; OPTIMAL APPROXIMATION; STOCHASTIC GRADIENT ASCENTS; STOCHASTIC GRADIENT DESCENT; STOCHASTIC OPTIMIZATIONS; SUBMODULAR FUNCTIONS; SUBMODULAR OPTIMIZATIONS;

STOCHASTIC MODELS;

EID: 85046998009     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (39)

1. Alexander A Ageev and Maxim I Sviridenko. Pipage rounding: A new method of constructing algorithms with proven performance guarantee. Journal of Combinatorial Optimization, 8(3): 307-328, 2004.
2. Francis Bach et al. Learning with submodular functions: A convex optimization perspective. Foundations and Trends® in Machine Learning, 6(2-3): 145-373, 2013.
3. Francis R. Bach. Convex analysis and optimization with submodular functions: a tutorial. CoRR, abs/1010.4207, 2010.
4. Ashwinkumar Badanidiyuru and Jan Vondrák. Fast algorithms for maximizing submodular functions. In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1497-1514. SIAM, 2014.
5. P. Brucker. An o(n) algorithm for quadratic knapsack problems. Operations Research Letters, 3 (3): 163-166, 1984.
6. Gruia Calinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák. Maximizing a submodular set function subject to a matroid constraint. In International Conference on Integer Programming and Combinatorial Optimization, pages 182-196. Springer, 2007.
7. Gruia Calinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák. Maximizing a monotone submodular function subject to a matroid constraint. SIAM Journal on Computing, 40(6): 1740-1766, 2011.
8. John Duchi, Elad Hazan, and Yoram Singer. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 2011.
9. Alina Ene and Huy L. Nguyen. Constrained submodular maximization: Beyond 1/e. pages 248-257, 2016.
10. Uriel Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4): 634-652, 1998.
11. Uriel Feige, Vahab S Mirrokni, and Jan Vondrak. Maximizing non-monotone submodular functions. SIAM Journal on Computing, 40(4): 1133-1153, 2011.
12. Moran Feldman, Joseph Naor, and Roy Schwartz. A unified continuous greedy algorithm for submodular maximization. In Foundations of Computer Science (FOCS), 2011 IEEE 52nd Annual Symposium on, pages 570-579. IEEE, 2011.
13. Marshall L Fisher, George L Nemhauser, and Laurence A Wolsey. An analysis of approximations for maximizing submodular set functions. In Polyhedral combinatorics, pages 73-87. Springer, 1978.
14. Natalie Glance, Matthew Hurst, Kamal Nigam, Matthew Siegler, Robert Stockton, and Takashi Tomokiyo. Deriving marketing intelligence from online discussion. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, pages 419-428, 2005.
15. th International Conference on Machine Learning, 2010.
16. Avinatan Hassidim and Yaron Singer. Submodular optimization under noise. CoRR, abs/1601.03095, 2016.
17. Thibaut Horel and Yaron Singer. Maximizing approximately submodular functions. NIPS, 2016.
18. Rishabh K Iyer and Jeff A Bilmes. Submodular optimization with submodular cover and submodular knapsack constraints. In Advances in Neural Information Processing Systems, pages 2436-2444, 2013.
19. Rishabh K. Iyer and Jeff A. Bilmes. Polyhedral aspects of submodularity, convexity and concavity. Arxiv, CoRR, abs/1506.07329, 2015.
20. th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 137-146, 2003.
21. Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. ICLR, 2015.
22. Andreas Krause and Daniel Golovin. Submodular function maximization. Tractability: Practical Approaches to Hard Problems, 3(19): 8, 2012.
23. Andreas Krause and Carlos Guestrin. Near-optimal nonmyopic value of information in graphical models. In Conference on Uncertainty in Artificial Intelligence (UAI), July 2005.
24. Andreas Krause and Carlos Guestrin. Near-optimal nonmyopic value of information in graphical models. In Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence, pages 324-331. AUAI Press, 2005.
25. Ariel Kulik, Hadas Shachnai, and Tami Tamir. Maximizing submodular set functions subject to multiple linear constraints. In Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 545-554. Society for Industrial and Applied Mathematics, 2009.
26. K. S. Sesh Kumar and Francis Bach. Active-set methods for submodular minimization problems. hal-01161759v3, 2016.
27. Hui Lin and Jeff Bilmes. A class of submodular functions for document summarization. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies-Volume 1, pages 510-520. Association for Computational Linguistics, 2011.
28. László Lovász. Submodular functions and convexity. In Mathematical Programming The State of the Art, pages 235-257. Springer, 1983.
29. Baharan Mirzasoleiman, Ashwinkumar Badanidiyuru, Amin Karbasi, Jan Vondrak, and Andreas Krause. Lazier than lazy greedy. Association for the Advancement of Artificial Intelligence, 2015.
30. George L. Nemhauser, Laurence A. Wolsey, and Marshall L. Fisher. An analysis of approximations for maximizing submodular set functions - i. Mathematical Programming, 14(1): 265-294, 1978.
31. P. M. Pardalos and N. Kovoor. An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds. Mathematical Programming, 46(1): 321-328, 1990.
32. Lior Seeman and Yaron Singer. Adaptive seeding in social networks. pages 459-468, 2013.
33. Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, 2014.
34. Adish Singla, Sebastian Tschiatschek, and Andreas Krause. Noisy submodular maximization via adaptive sampling with applications to crowdsourced image collection summarization. In Proc. Conference on Artificial Intelligence (AAAI), February 2016.
35. Matthew Streeter and Daniel Golovin. An online algorithm for maximizing submodular functions. NIPS, 2008.
36. Jan Vondrák. Submodularity in combinatorial optimization. Charles University, Prague, 2007.
37. Jan Vondrák. Optimal approximation for the submodular welfare problem in the value oracle model. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 67-74. ACM, 2008.
38. Jan Vondrák. Symmetry and approximability of submodular maximization problems. SIAM Journal on Computing, 42(1): 265-304, 2013.
39. Kai Wei, Rishabh Iyer, and Jeff Bilmes. Fast multi-stage submodular maximization. In International Conference on Machine Learning (ICML), Beijing, China, 2014.