Random zeroth-order gradient descent reaches ε-suboptimal solutions with probability 1-δ using O((dL/μ)log(1/ε) + log(1/δ)) queries deterministically and O(d log(1/ε)(log(1/ε)+log(1/δ))/ε) queries under bounded stochastic noise.
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High-Probability Guarantees for Random Zeroth-Order (Stochastic) Gradient Descent
Random zeroth-order gradient descent reaches ε-suboptimal solutions with probability 1-δ using O((dL/μ)log(1/ε) + log(1/δ)) queries deterministically and O(d log(1/ε)(log(1/ε)+log(1/δ))/ε) queries under bounded stochastic noise.