Query minimization under stochastic uncertainty

We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree find correct solution problem in consideration while minimizing expected total query show that, sorting problem, such found polynomial time. For of finding data item minimum value, we have some evidence hardness. This contradicts intuition, since easier both online setting adversarial inputs and offline verification setting. However, assumption leveraged beat deterministic randomized approximation lower bounds