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Gradient-Hessian Query Tradeoffs: Matching Lower Bounds in Logarithmic Dimension
We establish matching lower bounds for the tradeoff between gradient and Hessian queries in nonconvex optimization with Lipschitz Hessian. In normalized units, the initial objective gap is at most $T$, the Hessian Lipschitz constant is at most one, and the target gradient norm is one. For sufficient
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