Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids: From Robust Offline Optimization to Full-Bandit Learning

• URL: http://arxiv.org/abs/2608.12134v1
• Date: Wed, 12 Aug 2026 14:54:15 GMT
• Title: Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids: From Robust Offline Optimization to Full-Bandit Learning
• Abstract summary: We study the nonnegative submodular subject to a general matroid when the offline algorithm is given an arbitrary controlled value oracle.<n>Our algorithm retains limiting approximation factors $1/e$ for non-monotone objectives and $1-1/e$ for monotone objectives.<n>As a consequence, the offline-to-online reduction yields single-bandit CMAB algorithms for general matroid-constrained submodular rewards.
• Score: 55.29259818039367
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study nonnegative submodular maximization subject to a general matroid 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, 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, using $\widetilde O(nk^2\varepsilon^{-2})$ oracle calls. As a consequence, the offline-to-online reduction yields full-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.

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