arXiv:2609.10487v2 Announce Type: replace Abstract: We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but th...
arXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spect...
arXiv:2609. 20687v1 Announce Type: cross Abstract: 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 matching prior lower bounds up to logarithmic factors.
arXiv:2608. 04014v1 Announce Type: cross Abstract: The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering.
arXiv:2608. 15558v1 Announce Type: cross Abstract: For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p.
arXiv:2501.18183v3 Announce Type: replace-cross Abstract: We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-...
arXiv:2605.20434v2 Announce Type: replace-cross Abstract: We study the contradiction graphs associated with a binary concept class. For a class $H\subseteq\{0,1\}^X$, the order-$m$ contradiction grap...
arXiv:2607. 10751v1 Announce Type: new Abstract: Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$).
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv:2607. 23367v1 Announce Type: cross Abstract: We study whether strictly positive marginal values restore the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) for indivisible goods.
arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
arXiv:2609. 10981v1 Announce Type: new Abstract: Bakhtiari, Lattimore and Szepesv\'ari (COLT 2025) proved that Thompson sampling (TS) has Bayesian regret $\tilde O(d^{5/2}\sqrt n)$ for bandit convex optimisation with convex \emph{monotone} ridge losses $f(x)=\ell(\ip{x}{\theta})$, and asked whether monotonicity of the link is necessary.