Before revision: Soon after the seminal paper of Gittins, Peter Whittle demonstrated that the index emerges as a lagrangian multiplier from a dynamic programming formulation of the problem called retirement process and conjectured that the same index would be a good heuristic in a more general setup named Restless bandit.
After revision: Soon after the seminal paper of Gittins, Peter Whittle demonstrated that the index emerges as a Lagrange multiplier from a dynamic programming formulation of the problem called retirement process and conjectured that the same index would be a good heuristic in a more general setup named Restless bandit.