We establish the optimal query complexity of smooth convex quadratic optimization from exact function values. For dimension $d$, smoothness $L$, and minimizer radius $R$, the sharp rate at small relative error is $\Theta(d\min\{d,\sqrt{LR^2/\varepsilon}\})$. The lower bound has no logarithmic loss and holds even for ad...
Vadim Abronin, A. Gasnikov, D. Dvinskikh· 0 citations
We study the query complexity of optimization with exact scalar-value information. For globally $L$-smooth convex functions on $\mathbb R^d$ with a minimizer in a Euclidean ball of radius $R$, we prove the lower bound $\Omega(d\min\{d,\sqrt{LR^2/\varepsilon}\})$ for adaptive randomized algorithms in the stated accuracy...
Yuriy Dorn, D. Dvinskikh, Т. В. Логінов et al.· 0 citations
Optimal first-order methods on non-Euclidean domains such as the $\ell_1$ ball $B_1^n(R)=\{x\in\mathbb R^n:\|x\|_1\le R\}$ pair the prox-function with the norm in which smoothness is measured. When the gradient is $L$-Lipschitz in the Euclidean norm only, the accelerated method with a Euclidean prox-setup reduces the f...
Т. В. Логінов, A. Gasnikov, Yuriy Dorn et al.· 0 citations
A two-phase accelerated method that achieves, with high probability, an accelerated optimization contribution and smooth-subclass-optimal statistical dependence on accuracy, up to logarithmic and generalized-smoothness factors.
D. Dvinskikh, A. Gasnikov, A. Lobanov et al.· 1 citation
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