Online convex optimization in dynamic environments

IEEE Journal on Selected Topics in Signal Processing

Volumn 9, Issue 4, 2015, Pages 647-662

  Hall, Eric C ^a   Willett, Rebecca M ^b  

^a Duke University   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Dynamical Models; online Optimization; stochastic Filtering

Indexed keywords

ALGORITHMS; BIG DATA; CLUSTERING ALGORITHMS; COMPRESSED SENSING; CONVEX OPTIMIZATION; SOCIAL NETWORKING (ONLINE); STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

ANOMALOUS INFORMATION; COMPUTATIONALLY EFFICIENT; DYNAMICAL MODEL; HIGH DIMENSIONAL DATA; NON-STATIONARY ENVIRONMENT; ONLINE CONVEX OPTIMIZATIONS; ONLINE OPTIMIZATION; STOCHASTIC FILTERING;

E-LEARNING;

EID: 84929315531     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2015.2404790     Document Type: Article

References (63)

1. E. Hall and R. Willett, "Dynamical models and tracking regret in online convex programming," in Proc. Int. Conf. Mach. Learn. (ICML), 2013.
2. E. Dumbill, What is big data? an introduction to the big data landscape 2012 [Online]. Available: http://strata.oreilly.com/2012/01/what-isbig-data.html
3. W. Clavin, Managing the deluge of 'big data' from space 2013 [Online]. Available: http://www.jpl.nasa.gov/news/news.php?release= 2013-299
4. J. Matson, Scientific Amer "Nasa readies a satellite to probe the suninside and out," 2010 [Online]. Available: http://www.scientificamerican.com/article/solar-dynamics-observatory-sdo/
5. P. E. Dewdney, P. J. Hall, R. T. Schlilzzi, and T. J. L. W. Lazio, "The square kilometre array," Proc. IEEE, vol. 97, no. 8, pp. 1482-1496, Aug. 2009.
6. J. Marlow, "What to do with 1,000,000,000,000,000,000 bytes of astronomical data per day," 2012 [Online]. Available: http://www.wired.com/2012/04/what-to-do-with-1000000000000000000-bytes-of-astronomical-data-per-day/
7. A. Bain and D. Crisan, Fundamentals of stochastic filtering. New York, NY, USA: Springer, 2009.
8. L. Xie, Y. C. Soh, and C. E. de Souza, "Robust Kalman filtering for uncertain discrete-time systems," IEEE Trans. Autom. Control, vol. 39, no. 6, pp. 1310-1314, Jun. 1994.
9. Y. Theodor and U. Shaked, "Robust discrete-time minimum-variance filtering," IEEE Trans. Signal Process., vol. 44, no. 2, pp. 181-189, Feb. 1996.
10. N. Merhav and M. Feder, "Universal prediction," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2124-2147, Oct. 1998.
11. A. S. Nemirovsky and D. B. Yudin, Problem complexity and method efficiency in optimization. New York, NY, USA: Wiley, 1983.
12. A. Beck and M. Teboulle, "Mirror descent and nonlinear projected subgradient methods for convex programming," Operat. Res. Lett, vol. 31, pp. 167-175, 2003.
13. M. Zinkevich, "Online convex programming and generalized infinitesimal gradient descent," in Proc. Int. Conf. Mach. Learning (ICML), 2003, pp. 928-936.
14. N. Cesa-Bianchi and G. Lugosi, Prediction, learning and games. New York, NY, USA: Cambridge Univ. Press, 2006.
15. O. Banerjee, L. El Ghaoui, and A. d'Aspremont, "Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data," J. Mach. Learn. Res., vol. 9, pp. 485-516, 2008.
16. P. Ravikumar, M. J. Wainwright, and J. D. Lafferty, "High-dimenstional ising model selection using ℓ1-regularized logistic regression," Ann. Statist, vol. 38, pp. 1287-1319, 2010.
17. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, no. 8, pp. 1207-1223, 2006.
18. M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Comput, vol. 15, pp. 1373-1396, Jun. 2003.
19. D. Angelosante, J. A. Bazerque, and G. B. Giannakis, "Online adaptive estimation of sparse signals: Where RLS meets the 11-norm," IEEE Trans. Signal Process., vol. 58, no. 7, pp. 3436-3447, Jul. 2010.
20. M. Herbster and M. K. Warmuth, "Tracking the best linear predictor," J. Mach. Learn. Res, vol. 35, no. 3, pp. 281-309, 2001.
21. N. Cesa-Bianchi, P. Gaillard, G. Lugosi, and G. Stoltz, "A new look at shifting regret," ArXiv:1202.3323, 2012.
22. N. Littlestone and M. K. Warmuth, "The weighted majority algorithm," Inf. Comput, vol. 108, no. 2, pp. 212-261, 1994.
23. E. Hazan and C. Seshadhri, "Efficient learning algorithms for changing environments," in Proc. Int. Conf. Mach. Learn. (ICML), 2009, pp. 393-400.
24. L. M. Bregman, "The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming," Comput. Math. Math. Phys, vol. 7, pp. 200-217, 1967.
25. Y. Censor and S. A. Zenios, Parallel optimization: Theory, algorithms and applications. Oxford, U.K.: Oxford Univ. Press, 1997.
26. J. Duchi, S. Shalev-Shwartz, Y. Singer, and A. Tewari, "Composite objective mirror descent," in Proc. Conf. Learn. Theory (COLT), 2010.
27. L. Xiao, "Dual averaging methods for regularized stochastic learning and online optimization," J. Mach. Learn. Res, vol. 11, pp. 2543-2596, 2010.
28. J. Langford, L. Li, and T. Zhang, "Sparse online learning via truncated gradient," J. Mach. Learn. Res, vol. 10, pp. 777-801, 2009.
29. B. McMahan, "A unified view of regularized dual averaging and mirror descent with implicit updates," ArXiv:1009.3240v2, 2011.
30. S. Haykin, Adaptive filter theory. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
31. A. Rakhlin and K. Sridharan, "Online learning with predictable sequences," ArXiv:1208.3728, 2012.
32. M. Herbster and M. K. Warmuth, "Tracking the best expert," Mach. Learn., vol. 32, pp. 151-178, 1998.
33. W. Koolen and S. de Rooij, "Combining expert advice efficiently," in Proc. 21st Annu. Conf. Learn. Theory (COLT'08), 2008, pp. 275-286.
34. D. Adamskiy, W. M. Koolen, A. Chernov, and V. Vovk, "A closer look at adaptive regret," in Proc. 23rd Int. Conf. Algorithmic Learn. Theory, ALT'12, 2012, pp. 290-304.
35. A. Gyorgy, T. Linder, and G. Lugosi, "Efficient tracking of large classes of experts," IEEE Trans. Inf. Theory, vol. 58, no. 11, pp. 6709-6725, Nov. 2012.
36. V. Vovk, "Aggregating algorithms," in Proc. Conf. Learn. Theory (COLT), 1990.
37. C. Shalizi, A. Jacobs, K. Klikner, and A. Clauset, "Adapting to nonstationarity with growing expert ensembles," ArXiv:1103:0949, 2011.
38. S. Amari and H. Nagaoka, "Methods of information geometry," in Providence Amer. Math. Soc., 2000.
39. M. J. Wainwright and M. I. Jordan, "Graphical models, exponential families, and variational inference," Foundat. Trends Mach. Learn., vol. 1, pp. 1-305, Dec. 2008.
40. K. S. Azoury and M. K. Warmuth, "Relative loss bounds for on-line density estimation with the exponential family of distributions," Mach. Learn., vol. 43, pp. 211-246, 2001.
41. M. Raginsky, R. Willett, C. Horn, J. Silva, and R. Marcia, "Sequential anomaly detection in the presence of noise and limited feedback," IEEE Trans. Inf. Theory, vol. 58, no. 8, pp. 5544-5562, Aug. 2012.
42. J.-B Hiriart-Urruty and C. Lemaréchal, Fundamentals of convex analysis. Berlin, Germany: Springer, 2001.
43. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambrdige Univ. Press, 2004.
44. A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, "Robust stochastic approximation approach to stochastic programming," SIAM J. Optim, vol. 19, no. 4, pp. 1574-1609, 2009.
45. M. Szummer and R. W. Picard, "Temporal texture modeling," in Proc. Int. Conf. Image Process. (ICIP), 1996.
46. G. Doretto, A. Chiuso, Y. Wu, and S. Soatto, "Dynamic textures," Int. J. Comput. Vis., vol. 51, no. 2, pp. 91-109, 2003.
47. A. Ravichandran, R. Chaudhry, and R. Vidal, "Dynamic texture toolbox," 2011 [Online]. Available: http://www.vision.jhu.edu
48. V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, "Compressive fluorescence microscopy for biological and hyperspectral imaging," Proc. Nat. Acad. Sci., vol. 109, no. 26, pp. E1679-E1687, 2012.
49. R. Marcia and R. Willett, "Compressive coded aperture video reconstruction," in Proc. Eur. Signal Process. Conf. EUSIPCO, 2008.
50. J. Y. Park and M. B. Wakin, "A multiscale framework for compressive sensing of video," in Picture Coding Symp. (PCS), Chicago, IL, USA, May 2009.
51. A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, "CS-MUVI: video compressive sensing for spatial-multiplexing cameras," in Proc. IEEE Int. Conf. Comput. Photog. (ICCP), Apr. 2012, pp. 1-10.
52. D. Angelosante, G. B. Giannakis, and E. Grossi, "Compressed sensing of time-varying signals," in Proc. Int. Conf. Digital Signal Process., 2009.
53. N. Vaswani and W. Lu, "Modified-CS: Modifying compressive sensing for problems with partially known support," IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4595-4607, Sep. 2010.
54. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single pixel imaging via compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 83-91, Mar. 2008.
55. Z. Lin, M. Chen, and Y. Ma, "The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices," ArXiv:1009:5055, 2010.
56. C. Blundell, K. A. Heller, and J. M. Beck, "Modelling reciprocating relationships with Hawkes processes," in Proc. NIPS, 2012.
57. S. W. Linderman and R. P. Adams, "Discovering latent network structure in point process data," ArXiv:1402.0914, 2014.
58. A. Stomakhin, M. B. Short, and A. Bertozzi, "Reconstruction of missing data in social networks based on temporal patterns of interactions," Inverse Problems, vol. 27, no. 11, p. 115013, 2011.
59. E. N. Brown, R. E. Kass, and P. P. Mitra, "Multiple neural spike train data analysis: state-of-the-art and future challenges," Nature Neurosci., vol. 7, no. 5, pp. 456-461, 2004.
60. B. Klimt and Y. Yang, "The enron corpus: a new dataset for e-mail classification research," in Proc. Eur. Conf. Mach. Learn. (ECML), 2004, pp. 217-226.
61. Jun. 3, 2010. [Online]. Available: http://www.pbs.org/wgbh/pages/frontline/shows/blackout/california/timeline.html
62. R. Smith and J. Emswhwiller, "Enron faces collapse as Dynegy bolts and stock price, credit standing dive," Wall Street J, 2001.
63. J. M. Steele, The Cauchy-Schwarz Master Class : An Introduction to the Art of Mathematical Inequalities. New York, NY, USA: Cambridge Univ. Press, 2010.