Théo Paquier

Minimax optimality for sequential gradient-free minimization of smooth functions and their derivatives

We consider the problem of noisy gradient-free minimization of the k-th order partial derivative of a $\beta$-H{\"o}lder function supported on a d-dimensional cube. We show that T ^{($\beta$+d+k)/(2$\beta$+d)} log(T )^{(\beta-k)/(2\beta+d)} is a non-asymptotic minimax rate of the T step cumulative regret for all $\beta...