The minimax optimal rate for minimizing the k-th derivative of a Hölder function from noisy zero-order queries is N^{-(β-1)/(β+k)}, achieved by a kernel-based projected stochastic gradient algorithm.
and Dahleh, Munther A
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Gradient-free stochastic optimization of derivatives under strong convexity
The minimax optimal rate for minimizing the k-th derivative of a Hölder function from noisy zero-order queries is N^{-(β-1)/(β+k)}, achieved by a kernel-based projected stochastic gradient algorithm.