Control limits for two-state partially observable Markov decision processes

We prove that “dominance in expectation” (the expected profit is larger in the good state than in the bad state) suffices for the optimal policy to be of a CONTROL LIMIT (CLT) type: continue if and only if the good state probability exceeds the CLT. This condition is weaker than “stochastic dominance”, which has been prevailing. We also show that the “expected profit function” is convex, strictly increasing.