Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization

In three linesTheoretical paper establishing sharp lower bounds for higher-order smooth nonconvex optimization. Authors prove ε^(-7/4) rate under Lipschitz Hessians and ε^(-5/3) rate under third-order smoothness are optimal in first-order oracle complexity. Hard instance uses block-chain mechanism for blockwise oracle revelation.

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