Establishes matching Ω(ε^{-7/4}) and Ω(ε^{-5/3}) lower bounds via a block-chain construction for deterministic first-order methods under higher-order smoothness.
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cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Presents classical Õ(n²/ε^{1.5}) and quantum Õ(n/ε^{1.5}) query algorithms for ε-stationary points of twice-differentiable non-convex functions with Lipschitz gradient and Hessian via comparison oracles.
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Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization
Establishes matching Ω(ε^{-7/4}) and Ω(ε^{-5/3}) lower bounds via a block-chain construction for deterministic first-order methods under higher-order smoothness.
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Finding Stationary Points by Comparisons
Presents classical Õ(n²/ε^{1.5}) and quantum Õ(n/ε^{1.5}) query algorithms for ε-stationary points of twice-differentiable non-convex functions with Lipschitz gradient and Hessian via comparison oracles.