Characterization and computation of restless bandit marginal productivity indices
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Computing an index policy for bandits with switching penalties
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Queueing Systems: Theory and Applications
A Generalized Gittins Index for a Class of Multiarmed Bandits with General Resource Requirements
Mathematics of Operations Research
Computing an index policy for multiarmed bandits with deadlines
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Computing a Classic Index for Finite-Horizon Bandits
INFORMS Journal on Computing
Optimal index rules for single resource allocation to stochastic dynamic competitors
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Computing a Classic Index for Finite-Horizon Bandits
INFORMS Journal on Computing
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This paper presents a new fast-pivoting algorithm that computes the n Gittins index values of an n-state bandit---in the discounted and undiscounted cases---by performing (2/3)n3 + O(n2) arithmetic operations, thus attaining better complexity than previous algorithms and matching that of solving a corresponding linear-equation system by Gaussian elimination. The algorithm further applies to the problem of optimal stopping of a Markov chain, for which a novel Gittins-index solution approach is introduced. The algorithm draws on Gittins and Jones' (1974) index definition via calibration, on Kallenberg's (1986) proposal of using parametric linear programming, on Dantzig's simplex method, on the Varaiya et al. (1985) algorithm, and on the author's earlier work. This paper elucidates the structure of parametric simplex tableaux. Special structure is exploited to reduce the computational effort of pivot steps, decreasing the operation count by a factor of three relative to conventional pivoting, and by a factor of 3/2 relative to recent state-elimination algorithms. A computational study demonstrates significant time savings against alternative algorithms.