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We study the causal bandit problem that entails identifying a near-optimalintervention from a specified set $A$ of (possibly non-atomic) interventionsover a given causal graph. Here, an optimal intervention in ${A}$ is one thatmaximizes the expected value for a designated reward variable in the graph, andwe use the standard notion of simple regret to quantify near optimality.Considering Bernoulli random variables and for causal graphs on $N$ verticeswith constant in-degree, prior work has achieved a worst case guarantee of$\widetilde{O} (N/\sqrt{T})$ for simple regret. The current work utilizes theidea of covering interventions (which are not necessarily contained within${A}$) and establishes a simple regret guarantee of$\widetilde{O}(\sqrt{N/T})$. Notably, and in contrast to prior work, our simpleregret bound depends only on explicit parameters of the problem instance. Wealso go beyond prior work and achieve a simple regret guarantee for causalgraphs with unobserved variables. Further, we perform experiments to showimprovements over baselines in this setting.

Learning Good Interventions in Causal Graphs via Covering