We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$. (MG26) provides selectors with a movement bound for the problem of chasing high-dimensional convex nested sets for every $p<q$ and generally reduces Lipschitz convex optimization...
David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán et al.· arXiv.org· 1 citation
We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$. For $p<q$, we obtain error $\widetilde{O}_{p,q}(GR/T^{1/p-(1/q-1/2)_{+}})$ after $T$ or...
David Martínez-Rubio, Cristóbal Guzmán· 1 citation
We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p<q$) can improve convergence rates in convex optimization, and...
David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán et al.· 1 citation
The lower bound holds against any randomized algorithm that succeeds with constant probability and extends to settings with ``sparse''noise, ruling out the possibility of improving oracle complexity as a function of $\varepsilon$ by measuring variance in a non-matching $\ell_p$ norm.
Jelena Diakonikolas, Cristóbal Guzmán, David Martínez-Rubio· 0 citations
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