| This work introduces the "online probing" problem: In each round, the learner is able to purchase the values of a subset of features for the current instance. After the learner uses this information to produce a prediction for this instance, it then has the option of paying for seeing the full loss function for this instance that he is evaluated against. Either way, the learner pays for the errors of its predictions, and the cost of observing the features and loss function. We consider two variations of this problem, depending on whether the learner can observe the label for free. We provide algorithms and upper and lower bounds of the regret for both variants. We show that the paying a positive cost for the label significantly increases the regret of the problem. At the end we also convert the online algorithms to variants for batch settings. |
