English, Article, Journal or magazine article edition: Restless Bandits, Linear Programming Relaxations and a Primal-dual Index Heuristic Dimitris Bertsimas; José Niño-Mora

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Bookmark: http://trove.nla.gov.au/version/191827
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Restless Bandits, Linear Programming Relaxations and a Primal-dual Index Heuristic
Author
  • Dimitris Bertsimas
  • José Niño-Mora
Physical Description
  • preprint
Notes
  • We develop a mathematical programming approach for the classical PSPACE - hard restless bandit problem in stochastic optimization. We introduce a hierarchy of n (where n is the number of bandits) increasingly stronger linear programming relaxations, the last of which is exact and corresponds to the (exponential size) formulation of the problem as a Markov decision chain, while the other relaxations provide bounds and are efficiently computed. We also propose a priority-index heuristic scheduling policy from the solution to the first-order relaxation, where the indices are defined in terms of optimal dual variables. In this way we propose a policy and a suboptimality guarantee. We report results of computational experiments that suggest that the proposed heuristic policy is nearly optimal. Moreover, the second-order relaxation is found to provide strong bounds on the optimal value.
  • Stochastic scheduling, bandit problems, resource allocation, dynamic programming
  • RePEc:upf:upfgen:301
Language
  • English
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