Variance-Aware Bandit Framework for Dynamic Probabilistic Maximum Coverage Problem With Triggered or Self-Reliant Arms

The Probabilistic Maximum Coverage (PMC) problem plays a pivotal role in modeling various network applications, such as mobile crowdsensing, which involves selecting nodes within a graph that probabilistically cover other nodes. Our study focuses on PMC within the framework of online learning, termed the PMC bandit, where the network parameters are initially unknown. In this scenario, the decision-maker is tasked with learning these parameters to maximize the cumulative rewards from covered nodes. Despite prior research on the PMC bandit, we propose a novel variant, dynamic PMC-G bandit, which extends the semi-bandit feedback model to represent applications more accurately. To tackle the complexities of the time-varying combinatorial arm set rather than traditional static, we enhance the Combinatorial Upper Confidence Bound (CUCB) algorithms by developing two innovative variance-aware strategies: the Variance-Adaptive Combinatorial Upper Confidence Bound (VACUCB) for probabilistically triggered arms, and the Action-Based Combinatorial Upper Confidence Bound (ABCUCB) for self-reliant arms, i.e., independent arms with probabilistically triggered outcomes. Based on variance-aware properties, our contributions notably reduce the dependence on the number of nodes K selected per round, demonstrating that: (i) VACUCB effectively minimizes the regret associated with the triggered arms, enhancing the CUCB by a factor of $\tilde {O}(K)$ ; (ii) ABCUCB further diminishes the dependence on K in the leading term. Empirical results from synthetic and real-world datasets confirm that our proposed algorithms outperform current benchmarks in three network applications.