Learning with membership queries to minimize prediction error

In this paper, we consider the problem to predict the class of an unknown sample after learning from queries. We propose to evaluate a learning algorithm by a loss function for the prediction under a constraint. In this paper, the error probability for the prediction and the number of queries is defined as the loss function and the constraint, respectively. Then our objective is to minimize the error probability, the error probability is determined by what presentation order for instances to query and how to predict. Since the optimal prediction has been shown in previous researches, we only have to select the optimal presentation order for instances to query. We propose a lower bound used in the branch-and-bound algorithm to select the optimal presentation order for instances. Lastly, we show the efficiency of the algorithm using the derived lower bound by numerical computation.