Approximation algorithms for correlated knapsacks and non-martingale bandits

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2011, Pages 827-836

  Gupta, Anupam ^a   Krishnaswamy, Ravishankar ^a   Molinaro, Marco ^b   Ravi, R ^b  

^a Carnegie Mellon University   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Approximation Algorithms; Multi Armed Bandits; Stochastic Optimization

Indexed keywords

ADAPTIVE SCHEDULING ALGORITHM; CONSTANT FACTOR APPROXIMATION; FRACTIONAL SOLUTIONS; GAP FILLING; INTEGRALITY GAPS; LINEAR PROGRAMMING RELAXATION; LP RELAXATION; MULTI ARMED BANDIT; STOCHASTIC KNAPSACK PROBLEM; STOCHASTIC OPTIMIZATIONS; STOCHASTIC PACKING PROBLEMS; TIME ORDERING;

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION; COMPUTER SCIENCE; INTEGER PROGRAMMING; PROBABILITY DISTRIBUTIONS;

STOCHASTIC SYSTEMS;

EID: 84863332792     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2011.48     Document Type: Conference Paper

References (27)

1. D. P. Bertsekas, Dynamic programming and optimal control., 3rd ed. Athena Scientific, Belmont, MA, 2005.
2. D. Bertsimas and A. J. Mersereau, "A learning approach for interactive marketing to a customer segment," Operations Research, vol. 55, no. 6, pp. 1120-1135, 2007. (Pubitemid 351159521)
3. A. Bhalgat, A. Goel, and S. Khanna, "Improved approximation results for stochastic knapsack problems," in SODA, 2011.
4. J. R. Birge and F. Louveaux, Introduction to stochastic programming. Springer-Verlag, 1997.
5. D. Chakrabarti, R. Kumar, F. Radlinski, and E. Upfal, "Mortal multi-armed bandits," in NIPS, 2008, pp. 273-280.
6. S. Chawla and T. Roughgarden, "Single-source stochastic routing," in Proceedings of APPROX, 2006, pp. 82-94.
7. J. Coffman, E. G., L. Flatto, M. R. Garey, and R. R. Weber, "Minimizing expected makespans on uniform processor systems," Adv. Appl. Prob., vol. 19, no. 1, pp. pp. 177-201, 1987.
8. B. C. Dean, "Approximation algorithms for stochastic scheduling problems," Ph.D. dissertation, MIT, 2005.
9. B. C. Dean, M. X. Goemans, and J. Vondrák, "Adaptivity and approximation for stochastic packing problems," in SODA, 2005, pp. 395-404.
10. -, "Approximating the stochastic knapsack problem: The benefit of adaptivity," Math. Oper. Res., vol. 33, no. 4, pp. 945-964, 2008.
11. V. F. Farias and R. Madan, "The irrevocable multiarmed bandit problem," Oper. Res., vol. 59, no. 2, pp. 383-399, 2011.
12. J. C. Gittins, Multi-armed bandit allocation indices. John Wiley & Sons Ltd., 1989.
13. J. Gittins, K. Glazebrook, and R. Weber, Multi-armed Bandit Allocation Indices. Wiley Interscience, 2011.
14. A. Goel and P. Indyk, "Stochastic load balancing and related problems," in FOCS, 1999, pp. 579-586.
15. A. Goel, S. Khanna, and B. Null, "The ratio index for budgeted learning, with applications," in SODA, 2009, pp. 18-27.
16. S. Guha and K. Munagala, "Approximation algorithms for budgeted learning problems," in STOC, 2007, pp. 104-113, full version as Sequential Design of Experiments via Linear Programming, http://arxiv.org/abs/0805.2630v1.
17. -, "Model-driven optimization using adaptive probes," in SODA, 2007, pp. 308-317, full version as Adaptive Uncertainty Resolution in Bayesian Combinatorial Optimization Problems, http://arxiv.org/abs/0812.1012v1.
18. -, "Multi-armed bandits with metric switching costs," in ICALP, 2009, pp. 496-507.
19. S. Guha, K. Munagala, and M. Pal, "Iterated allocations with delayed feedback," ArXiv, vol. arxiv:abs/1011.1161, 2011.
20. S. Guha, K. Munagala, and P. Shi, "On index policies for restless bandit problems," CoRR, vol. abs/0711.3861, 2007, http://arxiv.org/abs/ 0711.3861. Full version of Approximation algorithms for partial-information based stochastic control with Markovian rewards (FOCS'07), and Approximation algorithms for restless bandit problems, (SODA'09).
21. A. Gupta, R. Krishnaswamy, M. Molinaro, and R. Ravi, "Approximation algorithms for correlated knapsacks and non-martingale bandits," CoRR, vol. abs/1102.3749, 2011.
22. J. Kleinberg, Y. Rabani, and É. Tardos, "Allocating bandwidth for bursty connections," SIAM J. Comput., vol. 30, no. 1, pp. 191-217, 2000.
23. A. J. Kleywegt and J. D. Papastavrou, "The dynamic and stochastic knapsack problem with random sized items," Oper. Res., vol. 49, pp. 26-41, January 2001.
24. R. H. Möhring, A. S. Schulz, and M. Uetz, "Approximation in stochastic scheduling: the power of lp-based priority policies,"JACM, vol. 46, no. 6, pp. 924-942, 1999.
25. M. Pinedo, Scheduling: Theory, Algorithms, and Systems. Prentice Hall, 1995.
26. H. Robbins, "Some aspects of the sequential design of experiments,"Bull. AMS, vol. 58, no. 5, pp. 527-535, 1952.
27. M. Skutella and M. Uetz, "Scheduling precedence-constrained jobs with stochastic processing times on parallel machines," in SODA, 2001, pp. 589-590.