Efficient Graph Bandit Learning with Side-Observations and Switching Constraints

This paper presents a novel framework for multi-armed bandit problems with side-observations and switching constraints, which arises in a range of real-world applications such as robotic. To address the challenges of effectively utilizing graph-structured observations while adhering to graph constraints, we design graph-agnostic and graph-aware algorithms tailored to this new setting. Specifically, our graph-agnostic algorithm selects nodes with the highest upper confidence bound without prior knowledge of feedback probabilities, while minimizing switching costs using offline shortest path planning and the doubling trick. If the graph structure and associated probability matrix are known, our graph-aware algorithm plans the exploration step using a linear programming approach and eliminates suboptimal nodes iteratively. We rigorously analyze the performance of our proposed algorithms, providing near-optimal minimax and instance-dependent regret upper bounds. Our analysis shows that our algorithms outperform generic reinforcement learning methods in terms of both regret and computational efficiency. Extensive numerical experiments on various types of graphs, including two real-world datasets, demonstrate the efficacy of our proposed methods and their advantages over benchmark methods in graph bandit settings.