חסמים גאומטריים למקסימיזציה מונוטונית DR-Submodular

תקציר מקורי באנגליתarXiv:2610.00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets. A learner commits each action before observing its objective and competes with the best fixed action in hindsight. We prove a comparator-uniform first-order inequality that gives coefficient $4/9$, improving the online $0.401$ benchmark, with one gradient query and one projection per round and $O(\sqrt T)$ expected approximate regret. If $\zeta {\bf 1} \in K\subseteq[0,1]^d$, the coefficient improves to $\underline\alpha(\zeta)=\tfrac12-(1-2\zeta)_+^2/[2(3-2\zeta)^2]$. The proof is a direct ordered-coordinate argument with an objective-independent rational action. Conversely, a three-group symmetry-gap constructi