Feedback graph regret bounds for Thompson Sampling and UCB
This provides theoretical insights for bandit algorithms in structured feedback settings, but it is incremental as it extends known algorithms to a specific feedback model.
The paper tackles the stochastic multi-armed bandit problem with graph-based feedback by analyzing Thompson Sampling and UCB algorithms, showing they achieve regret guarantees that incorporate graph structure and arm gaps without explicitly using the graph for exploration.
We study the stochastic multi-armed bandit problem with the graph-based feedback structure introduced by Mannor and Shamir. We analyze the performance of the two most prominent stochastic bandit algorithms, Thompson Sampling and Upper Confidence Bound (UCB), in the graph-based feedback setting. We show that these algorithms achieve regret guarantees that combine the graph structure and the gaps between the means of the arm distributions. Surprisingly this holds despite the fact that these algorithms do not explicitly use the graph structure to select arms; they observe the additional feedback but do not explore based on it. Towards this result we introduce a "layering technique" highlighting the commonalities in the two algorithms.