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- W3046823245 abstract "We establish improved rates for structured emph{non-smooth} optimization problems by means of near-optimal higher-order accelerated methods. In particular, given access to a standard oracle model that provides a $p^{th}$ order Taylor expansion of a emph{smoothed} version of the function, we show how to achieve $eps$-optimality for the emph{original} problem in $tilde{O}_ppa{eps^{-frac{2p+2}{3p+1}}}$ calls to the oracle. Furthermore, when $p=3$, we provide an efficient implementation of the near-optimal accelerated scheme that achieves an $O(eps^{-4/5})$ iteration complexity, where each iteration requires $tilde{O}(1)$ calls to a linear system solver. Thus, we go beyond the previous $O(eps^{-1})$ barrier in terms of $eps$ dependence, and in the case of $ell_infty$ regression and $ell_1$-SVM, we establish overall improvements for some parameter settings in the moderate-accuracy regime. Our results also lead to improved high-accuracy rates for minimizing a large class of convex quartic polynomials." @default.
- W3046823245 created "2020-08-07" @default.
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- W3046823245 date "2020-07-15" @default.
- W3046823245 modified "2023-09-28" @default.
- W3046823245 title "Highly smooth minimization of non-smooth problems" @default.
- W3046823245 hasPublicationYear "2020" @default.
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