Before revision:  We also show that this new technique provides optimal regret (up to log factors) in the linear case (i. e. the original contextual search problem), improving the previously known bound of \rightarrow Y in a certain hypothesis class H. We provide a generic algorithm with } O(d ^4) to O(d \log d) . Finally, we extend these results to a \tilde{O} noisy feedback model, where each round our feedback is flipped with  fixed probability p < 1/2.
After revision:  We also show that this new technique provides optimal regret (up to log factors) in the linear case (i. e. the original contextual search problem), improving the previously known bound of \rightarrow Y in a certain hypothesis class H. We provide a generic algorithm with } O(d ^2) regret where d is the covering dimension of this class. This leads in particular to a \tilde{O} noisy feedback model, where each round our feedback is flipped with fixed probability p < 1/2.