Systems and methods are disclosed for classifying histological tissues or specimens with two phases. In a first phase, the method includes providing off-line training using a processor during which one or more classifiers are trained based on examples, including: finding a split of features into sets of increasing computational cost, assigning a computational cost to each set; training for each set of features a classifier using training examples; training for each classifier, a utility function that scores a usefulness of extracting the next feature set for a given tissue unit using the training examples. In a second phase, the method includes applying the classifiers to an unknown tissue sample with extracting the first set of features for all tissue units; deciding for which tissue unit to extract the next set of features by finding the tissue unit for which a score: S=U−h*C is maximized, where U is a utility function, C is a cost of acquiring the feature and h is a weighting parameter; iterating until a stopping criterion is met or no more feature can be computed; and issuing a tissue-level decision based on a current state.