We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to Question 2 from Stone (1982) on the optimal convergence rate within this model. The procedure constructed here has strong adaptation properties: it adapts both to the smoothness of the link function and to the unknown index. Moreover, the procedure locally adapts to the distribution of the data, which allows to prove the results for a fairly general design. The behavior of this algorithm is studied through numerical simulations. In particular, we show empirically that it improves strongly empirical risk minimization.