Comments on: Dynamic priority allocation via restless bandit marginal productivity indices

Jose Nino-Mora has given us a very nice survey of his results for theoretical and algorithm aspects of restless bandit indexation. His paper has inspired me to contribute some new results, which I will report in three parts. Firstly, I present an extension to restless bandits in which there are more than two possible actions in each state. Secondly, I show that condition (ii) in the definition of PCL(F)-indexability is actually implied by (i), if we add a mild condition that can always be met by perturbing the data. Thirdly, I describe two interesting classes of restless bandits that are always indexable.