Gittins index proof The strategy that plays the arm with the highest tax (until the optimal stopping time) is equivalent to the strategy that plays the arm with the highest Gittins index Gj (if Gj was the highest and it increases, then with optimal stopping, we would continue to play j).

The "index policy" induced by the Gittins index, consisting of choosing at any time the stochastic process with the currently highest Gittins index, is the solution of some stopping problems such as the one of dynamic allocation, where a decision-maker has to maximize the total reward by distributing a limited amount ...