Bandit Submodular Maximization under Matroid Constraints: Learning Compressed Exchange Policy

2026-08-25

AI Summary

研究了在拟阵约束下对抗性带状子模最大化问题，通过学习压缩交换策略，提出了一种具有次线性遗憾界的多项式时间算法。

Abstract

We study adversarial bandit maximization of monotone submodular functions under a matroid constraint. For a rank-$k$ matroid on $n$ elements, we give a randomized oracle-polynomial algorithm that makes one feasible value query per round and has expected $(1-1/e)$-regret $\widetilde O(n^{1/3}k^{2/3}T^{2/3})$. This is the first sublinear-regret algorithm for adversarial bandit submodular maximization under general matroid constraints. Technically, we view the problem as learning an exchange policy for the Poisson base walk. This connects the problem to contextual bandits and gives an information-theoretic sublinear-regret guarantee, but directly learning the exponentially many policies requires exponential time and space. We therefore introduce \emph{balanced fractional exchanges}, which compress the policy mixture into a single fractional base while retaining the exchange information needed by the Poisson analysis. This leads to an polynomial time algorithm with the same regret guarantee.

Problem

• adversarial bandit
• submodular maximization
• matroid constraint

Innovation

• adversarial bandit submodular maximization
• matroid constraints
• balanced fractional exchanges
• contextual bandits