Continuous Multi-Armed Bandits and Multiparameter Processes

A general framework is proposed for continuous time dynamic allocation models of a scarce resource among competing projects. The allocation model is formulated as a multi-armed bandit model and solved as a control problem of a multiparameter process. In contrast to discrete time bandits, where only one arm can be pulled at a time, the continuous time bandit must allow simultaneous pulls. The multiparameter approach allows a strong solution of diffusion-type bandits. Here the main problem is to define precisely how to switch among arms and the solution involves local times.