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) .
After revision:  The Steiner polynomial is a degree d polynomial with intrinsic volumes as the coefficients. We also study a generalized version of contextual search where the hidden linear function over the Euclidean space is replaced by a hidden function f : \mathcal{X \rightarrow Y in a certain hypothesis class H. We provide a generic algorithm with } O(d ^4) to O(d \log d) .