We resolve the problem of unweighted online stochastic matching with a known arrival law by establishing its optimal competitive ratio. For Poisson arrivals, we achieve $1-e/e^e\approx0.8206$, matching the upper bound of Chierichetti, Giacchini, Panconesi, and Vattani [ICALP 2025]. For exactly $n$ i.i.d.~arrivals, we o...
Paul Dütting, Michal Feldman, Mathieu Molina· 0 citations
We initiate the study of $\alpha$-fair prophet inequalities. This interpolates between utilitarian welfare $(\alpha=0)$, Nash welfare $(\alpha=1)$, and Rawlsian max-min fairness $(\alpha\to\infty)$. Given the non-linearity of the objective, it matters when the expectation is applied. For instance, for the Rawlsian obje...
Paul Duetting, Michal Feldman, Mathieu Molina· 0 citations
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 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
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