Robust intensity control with multiple levels of model uncertainty and the dual risk-sensitive problem

In this paper, we consider robust intensity control of a stochastic discrete event system. We introduce the notion of generalized relative entropy and extend the classical “entropy-based” approached to stochastic robust control by allowing for different levels of model uncertainty for different parts of the model. We also introduce a new class of risk-sensitive control problems which are characterized by multiple risk-sensitivity parameters and reward sharing terms, and show that it is equivalent to the robust control problem under an appropriate choice of reward sharing rule. This extends the well know duality between robust and risk-sensitive control the the case when there are multiple levels of model uncertainty within the same model.