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- W4308482813 abstract "We study the complexity of optimizing highly smooth convex functions. For a positive integer $p$, we want to find an $epsilon$-approximate minimum of a convex function $f$, given oracle access to the function and its first $p$ derivatives, assuming that the $p$th derivative of $f$ is Lipschitz. Recently, three independent research groups (Jiang et al., PLMR 2019; Gasnikov et al., PLMR 2019; Bubeck et al., PLMR 2019) developed a new algorithm that solves this problem with $tilde{O}(1/epsilon^{frac{2}{3p+1}})$ oracle calls for constant $p$. This is known to be optimal (up to log factors) for deterministic algorithms, but known lower bounds for randomized algorithms do not match this bound. We prove a new lower bound that matches this bound (up to log factors), and holds not only for randomized algorithms, but also for quantum algorithms." @default.
- W4308482813 created "2022-11-12" @default.
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- W4308482813 date "2021-12-02" @default.
- W4308482813 modified "2023-09-26" @default.
- W4308482813 title "Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness" @default.
- W4308482813 doi "https://doi.org/10.48550/arxiv.2112.01118" @default.
- W4308482813 hasPublicationYear "2021" @default.
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