发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对拟阵约束的子模最大化问题，证明了SGS-Poisson算法的对抗鲁棒性，并将其归约得到具有特定近似-遗憾因子的全臂赌博机CMAB算法。
AI 中文摘要
我们研究离线算法获得任意受控值神谕时，受一般拟阵约束的非负子模最大化问题。主要结果是针对恶意贪心交换泊松过程（Spiteful Greedy Swap Poisson Process，SGS-Poisson）的对抗鲁棒性定理：该算法无需修改其泊松强度、单元素交换规则或恶意丢弃步，即可对非单调目标保持极限近似因子1/e，对单调目标保持极限近似因子1-1/e。更精确地说，在每个满足对任意集合S有|f̂(S)-f(S)|≤ξ的受控神谕f̂下，我们的实现返回的可行集期望值至少分别为(1/e-ε)OPT-O(kξ)和(1-1/e-ε)OPT-O(kξ)，使用Õ(nk²ε⁻²)次神谕调用。由此，离线到在线的归约可得到针对一般拟阵约束子模奖励的全臂赌博机（full-bandit）CMAB算法，其极限近似-遗憾因子精确为1/e和1-1/e，遗憾为Õ(n^(1/5)k^(4/5)T^(4/5))。
英文摘要
We study nonnegative submodular maximization on $n$ elements subject to a general matroid of rank $k$, when the offline algorithm is given an arbitrary controlled value oracle. Our main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors $1/e$ for non-monotone objectives and $1-1/e$ for monotone objectives. More precisely, given an error bound $ξ\ge0$, under every controlled oracle $\widehat f$ satisfying $|\widehat f(S)-f(S)|\le ξ$ for every set $S$, our implementation returns a feasible set with expected value at least $(1/e-\varepsilon)OPT-O(kξ)$ and $(1-1/e-\varepsilon)OPT-O(kξ)$, respectively, where $OPT$ is the feasible optimum. The implementation uses a \emph{deterministically bounded} budget of $O(nk^{2}\varepsilon^{-2}\log n\log^{2}(1/\varepsilon))$ oracle calls. As a consequence, an offline-to-online reduction yields full-bandit combinatorial multi-armed bandit (CMAB) algorithms for general matroid-constrained submodular rewards with exact limiting approximation-regret factors $1/e$ and $1-1/e$ and $\widetilde O(n^{1/5}k^{4/5}T^{4/5})$ regret over $T$ rounds. These online guarantees allow exploration to play sets that become independent after deleting at most one element; exploitation and the benchmark remain matroid-feasible. For unit-capacity partition matroids we obtain $\widetilde O(n^{1/5}k^{3/5}T^{4/5})$ under the same exploration relaxation. We establish a deterministic query budget by truncating the Poisson process and identify the enlarged action set needed to answer its offline queries.
