Before revision: We study a general version of the problem of online learning under binary feedback: there is a hidden function f : \mathcal{X \rightarrow Y in a certain hypothesis class H. A learner is given adversarially chosen inputs (contexts) x_t \in X and is asked to submit a guess y_t \in Y for the value f(x_t).
After revision:  \rightarrow Y in a certain hypothesis class H. A learner is given adversarially chosen inputs (contexts) x_t \in X and is asked to submit a guess y_t \in Y for the value f(x_t).