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.· 0 citations
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
Minimizing gradients of a convex function is an important problem across optimization and learning tasks. The gradient provides a directly computable certificate of approximate stationarity, and its minimization usually implies stronger results than those for minimization of function values. In this work, we study grad...
Nico Pelleriti, Maryam Shiran, David Martínez-Rubio et al.· 0 citations
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