Causal Bandits with Unknown Graph Structure
This addresses a key limitation in causal bandit research for applications where graph structure is unknown, though it is incremental as it builds on prior work by removing a restrictive assumption.
The paper tackles the problem of causal bandits where existing methods require full knowledge of the causal graph structure, which is impractical, and develops novel algorithms that work without this knowledge for various graph types, showing regret guarantees that improve upon standard multi-armed bandit algorithms under mild conditions.
In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly improve upon those of standard multi-armed bandit (MAB) algorithms under mild conditions. Lastly, we prove our mild conditions are necessary: without them one cannot do better than standard MAB algorithms.