Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Randomized Greedy Methods for Weak Submodular Sensor Selection with Robustness Considerations (2404.03740v1)

Published 4 Apr 2024 in math.OC, cs.SY, eess.SP, and eess.SY

Abstract: We study a pair of budget- and performance-constrained weak submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the standard greedy procedure which explores the entire feasible search space. We propose a pair of stochastic greedy algorithms, namely, Modified Randomized Greedy (MRG) and Dual Randomized Greedy (DRG) to approximately solve the budget- and performance-constrained problems, respectively. For both algorithms, we derive approximation guarantees that hold with high probability. We then examine the use of DRG in robust optimization problems wherein the objective is to maximize the worst-case of a number of weak submodular objectives and propose the Randomized Weak Submodular Saturation Algorithm (Random-WSSA). We further derive a high-probability guarantee for when Random-WSSA successfully constructs a robust solution. Finally, we showcase the effectiveness of these algorithms in a variety of relevant uses within the context of Earth-observing LEO constellations which estimate atmospheric weather conditions and provide Earth coverage.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. M. G. Damavandi, V. Krishnamurthy, and J. R. Martí, “Robust meter placement for state estimation in active distribution systems,” IEEE Transactions on Smart Grid, vol. 6, no. 4, pp. 1972–1982, 2015.
  2. Z. Liu, A. Clark, P. Lee, L. Bushnell, D. Kirschen, and R. Poovendran, “Towards scalable voltage control in smart grid: a submodular optimization approach,” in Proceedings of the 7th International Conference on Cyber-Physical Systems, p. 20, IEEE Press, 2016.
  3. N. Buchbinder, M. Feldman, J. S. Naor, and R. Schwartz, “Submodular maximization with cardinality constraints,” in Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’14, (USA), p. 1433–1452, Society for Industrial and Applied Mathematics, 2014.
  4. S. Dughmi, T. Roughgarden, and M. Sundararajan, “Revenue submodularity,” in Auctions, Market Mechanisms and Their Applications (S. Das, M. Ostrovsky, D. Pennock, and B. Szymanksi, eds.), (Berlin, Heidelberg), pp. 89–91, Springer Berlin Heidelberg, 2009.
  5. A. S. Schulz and N. A. Uhan, “Approximating the least core value and least core of cooperative games with supermodular costs,” Discrete Optimization, vol. 10, no. 2, pp. 163–180, 2013.
  6. G. Attigeri, M. Manohara Pai, and R. M. Pai, “Feature selection using submodular approach for financial big data,” Journal of Information Processing Systems, vol. 15, no. 6, pp. 1306–1325, 2019.
  7. R. A. Richards, R. T. Houlette, J. L. Mohammed, et al., “Distributed satellite constellation planning and scheduling.,” in FLAIRS Conference, pp. 68–72, 2001.
  8. D. P. Williamson and D. B. Shmoys, The design of approximation algorithms. Cambridge university press, 2011.
  9. G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher, “An analysis of approximations for maximizing submodular set functions,” Mathematical Programming, vol. 14, no. 1, pp. 265–294, 1978.
  10. L. A. Wolsey, “An analysis of the greedy algorithm for the submodular set covering problem,” Combinatorica, vol. 2, no. 4, pp. 385–393, 1982.
  11. S. Khuller, A. Moss, and J. S. Naor, “The budgeted maximum coverage problem,” Information processing letters, vol. 70, no. 1, pp. 39–45, 1999.
  12. B. Mirzasoleiman, A. Badanidiyuru, A. Karbasi, J. Vondrak, and A. Krause, “Lazier than lazy greedy,” in AAAI Conference on Artificial Intelligence, AAAI, 2015.
  13. A. Hashemi, M. Ghasemi, H. Vikalo, and U. Topcu, “Randomized greedy sensor selection: Leveraging weak submodularity,” IEEE Transactions on Automatic Control, vol. 66, no. 1, pp. 199–212, 2021.
  14. A. Krause and D. Golovin, “Submodular function maximization,” in Tractability: Practical Approaches to Hard Problems, pp. 71–104, Cambridge University Press, 2014.
  15. M. Hibbard, A. Hashemi, T. Tanaka, and U. Topcu, “Randomized greedy algorithms for sensor selection in large-scale satellite constellations,” Proceedings of the American Control Conference, 2023.
  16. A. Poghosyan and A. Golkar, “CubeSat evolution: Analyzing CubeSat capabilities for conducting science missions,” Progress in Aerospace Sciences, vol. 88, pp. 59–83, 2017.
  17. K. M. Wagner, K. K. Schroeder, and J. T. Black, “Distributed space missions applied to sea surface height monitoring,” Acta Astronautica, vol. 178, pp. 634–644, 2021.
  18. K. Cahoy and A. K. Kennedy, “Initial results from ACCESS: an autonomous CubeSat constellation scheduling system for Earth observation,” 2017.
  19. W. J. Blackwell, S. Braun, R. Bennartz, C. Velden, M. DeMaria, R. Atlas, J. Dunion, F. Marks, R. Rogers, B. Annane, et al., “An overview of the TROPICS NASA Earth venture mission,” Quarterly Journal of the Royal Meteorological Society, vol. 144, pp. 16–26, 2018.
  20. C. Boshuizen, J. Mason, P. Klupar, and S. Spanhake, “Results from the planet labs flock constellation,” 2014.
  21. D. Selva and D. Krejci, “A survey and assessment of the capabilities of CubeSats for Earth observation,” Acta Astronautica, vol. 74, pp. 50–68, 2012.
  22. D. Mandl, G. Crum, V. Ly, M. Handy, K. F. Huemmrich, L. Ong, B. Holt, and R. Maharaja, “Hyperspectral CubeSat constellation for natural hazard response,” in Annual AIAA/USU Conference on Small Satellites, no. GSFC-E-DAA-TN33317, 2016.
  23. G. Santilli, C. Vendittozzi, C. Cappelletti, S. Battistini, and P. Gessini, “CubeSat constellations for disaster management in remote areas,” Acta Astronautica, vol. 145, pp. 11–17, 2018.
  24. S. Nag, J. L. Rios, D. Gerhardt, and C. Pham, “CubeSat constellation design for air traffic monitoring,” Acta Astronautica, vol. 128, pp. 180–193, 2016.
  25. S. Wu, W. Chen, C. Cao, C. Zhang, and Z. Mu, “A multiple-CubeSat constellation for integrated earth observation and marine/air traffic monitoring,” Advances in Space Research, vol. 67, no. 11, pp. 3712–3724, 2021.
  26. S. Siewert and L. McClure, “A system architecture to advance small satellite mission operations autonomy,” 1995.
  27. A. Hashemi, M. Ghasemi, H. Vikalo, and U. Topcu, “A randomized greedy algorithm for near-optimal sensor scheduling in large-scale sensor networks,” in American Control Conference (ACC), pp. 1027–1032, IEEE, 2018.
  28. U. Feige, “A threshold of ln n for approximating set cover,” Journal of the ACM, vol. 45, no. 4, pp. 634–652, Jul. 1998.
  29. H. Zhang and Y. Vorobeychik, “Submodular optimization with routing constraints,” in AAAI Conference on Artificial Intelligence, 2016.
  30. L. Chamon and A. Ribeiro, “Approximate supermodularity bounds for experimental design,” in Advances in Neural Information Processing Systems (NIPS), pp. 5409–5418, 2017.
  31. A. Hashemi, M. Ghasemi, and H. Vikalo, “Submodular observation selection and information gathering for quadratic models,” in Proceedings of the 36th International Conference on Machine Learning, vol. 97, 2019.
  32. A. Das and D. Kempe, “Submodular meets spectral: Greedy algorithms for subset selection, sparse approximation and dictionary selection,” in Proceedings of the International Conference on Machine Learning (ICML), pp. 1057–1064, 2011.
  33. E. R. Elenberg, R. Khanna, A. G. Dimakis, and S. Negahban, “Restricted strong convexity implies weak submodularity,” The Annals of Statistics, vol. 46, no. 6B, pp. 3539–3568, 2018.
  34. T. Horel and Y. Singer, “Maximization of approximately submodular functions,” in Advances in Neural Information Processing Systems (NIPS), pp. 3045–3053, 2016.
  35. A. A. Bian, J. M. Buhmann, A. Krause, and S. Tschiatschek, “Guarantees for greedy maximization of non-submodular functions with applications,” in International Conference on Machine Learning (ICML), pp. 498–507, Omnipress, 2017.
  36. R. Khanna, E. Elenberg, A. Dimakis, S. Negahban, and J. Ghosh, “Scalable greedy feature selection via weak submodularity,” in Artificial Intelligence and Statistics, pp. 1560–1568, 2017.
  37. M. Ghasemi, A. Hashemi, U. Topcu, and H. Vikalo, “On submodularity of quadratic observation selection in constrained networked sensing systems,” in 2019 American Control Conference (ACC), pp. 4671–4676, IEEE, 2019.
  38. A. Hashemi, H. Vikalo, and G. de Veciana, “On the performance-complexity tradeoff in stochastic greedy weak submodular optimization,” in ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3540–3544, IEEE, 2021.
  39. A. Hashemi, H. Vikalo, and G. de Veciana, “On the benefits of progressively increasing sampling sizes in stochastic greedy weak submodular maximization,” IEEE Transactions on Signal Processing, vol. 70, pp. 3978–3992, 2022.
  40. A. Hassidim and Y. Singer, “Robust guarantees of stochastic greedy algorithms,” in International Conference on Machine Learning, pp. 1424–1432, PMLR, 2017.
  41. F. Chung and L. Lu, “Concentration inequalities and martingale inequalities: a survey,” Internet Mathematics, vol. 3, no. 1, pp. 79–127, 2006.
  42. K. D. Harris, “The martingale z-test,” 2022.
  43. A. Das and D. Kempe, “Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection,” Journal of Machine Learning Research, vol. 19, no. 3, pp. 1–34, 2018.
  44. A. Krause, H. B. McMahan, C. Guestrin, and A. Gupta, “Robust submodular observation selection,” Journal of Machine Learning Research, vol. 9, no. 93, pp. 2761–2801, 2008.
  45. J. G. Walker, “Satellite constellations,” Journal of the British Interplanetary Society, vol. 37, p. 559, 1984.
  46. E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of atmospheric sciences, vol. 20, no. 2, pp. 130–141, 1963.
  47. John Wiley & Sons, 2004.
  48. Princeton university press, 2009.
  49. A. Ben-Tal and A. Nemirovski, “Robust optimization–methodology and applications,” Mathematical programming, vol. 92, pp. 453–480, 2002.
  50. R. Udwani, “Multi-objective maximization of monotone submodular functions with cardinality constraint,” in Advances in Neural Information Processing Systems (S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, eds.), vol. 31, Curran Associates, Inc., 2018.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now