Control of a Markov process in a problem with constraints (Q922966)

Given is a discrete-time Markov decision process with finite state and action space and \(\beta\)-discounted total reward F. Let \(\pi\) be a (randomized) strategy. In contrast to the usual approach it is searched for \(v=\sup_{\pi}E^{\pi}F\) under the constraints \(E^{\pi}F_ i\leq K_ i\), \(i=1,...,m\), for some functions \(F_ i\) and real constants \(K_ i\). Then there exists an optimal strategy which is a mixture of at most \(m+1\) stationary strategies.