arXiv AI
Sep 3

Online Non-Monotone DR-Submodular Maximization Matching the Offline $0.401$ Factor

The paper presents an online algorithm that achieves the same $0.401$ approximation factor for maximizing nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube as the best known offline construction. In the full-information value-oracle model, the algorithm attains this factor with sublinear regret, using $O(dT^{1/4})$ oracle calls per round and $O(T^{3/4})$ regret, and offers flexible batching trade-offs. Under a positive-anchor condition, a randomized blocking strategy preserves the $0.401$ factor while achieving $O(T^{5/6})$ one-point bandit regret.

By Vaneet Aggarwal, Yiyang Lu
Hugging Face Trending Papers
Sep 17

Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates

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 $T$ oracle queries, efficiently realizing the nearly optimal rates of (MBG+26), thereby resolving the nonsmooth end of the COLT 2015 open problem (Guz15b).