Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-19T15:49:33.996Z Has data issue: false hasContentIssue false

Restless bandits: activity allocation in a changing world

Published online by Cambridge University Press:  14 July 2016


We consider a population of n projects which in general continue to evolve whether in operation or not (although by different rules). It is desired to choose the projects in operation at each instant of time so as to maximise the expected rate of reward, under a constraint upon the expected number of projects in operation. The Lagrange multiplier associated with this constraint defines an index which reduces to the Gittins index when projects not being operated are static. If one is constrained to operate m projects exactly then arguments are advanced to support the conjecture that, for m and n large in constant ratio, the policy of operating the m projects of largest current index is nearly optimal. The index is evaluated for some particular projects.

Part 6 - The Analysis of Stochastic Phenomena
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Gittins, J. C. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. B 41, 148164.Google Scholar
Gittins, J. C. and Jones, D. M. (1974) A dynamic allocation index for the sequential design of experiments. In Progress in Statistics ed. Gani, J., North-Holland, Amsterdam, 241266.Google Scholar
Weiss, G. (1987) Approximation in results in parallel machines stochastic scheduling. Presented at the Twelfth Symposium on Operations Research, Passau.Google Scholar
Whittle, P. (1980) Multi-armed bandits and the Gittins index. J. R. Statist. Soc. B 42, 142149.Google Scholar
Whittle, P. (1981) Arm-acquiring bandits. Ann. Prob. 9, 284292.CrossRefGoogle Scholar
Whittle, P. (1984) Optimal routing in Jackson networks. Asia-Pacific J. Operat. Res. 1, 3237.Google Scholar
Whittle, P. (1986) Systems in Stochastic Equilibrium . Wiley, Chichester.Google Scholar