Learning Good Interventions in Causal Graphs via Covering
This provides a more efficient algorithm for selecting interventions in causal inference, with incremental improvements in regret bounds and applicability.
The paper tackles the causal bandit problem of identifying near-optimal interventions in causal graphs, achieving a simple regret bound of Õ(√(N/T)) that improves upon prior work by depending only on explicit parameters and extending to graphs with unobserved variables.
We study the causal bandit problem that entails identifying a near-optimal intervention from a specified set $A$ of (possibly non-atomic) interventions over a given causal graph. Here, an optimal intervention in ${A}$ is one that maximizes the expected value for a designated reward variable in the graph, and we use the standard notion of simple regret to quantify near optimality. Considering Bernoulli random variables and for causal graphs on $N$ vertices with constant in-degree, prior work has achieved a worst case guarantee of $\widetilde{O} (N/\sqrt{T})$ for simple regret. The current work utilizes the idea 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 simple regret bound depends only on explicit parameters of the problem instance. We also go beyond prior work and achieve a simple regret guarantee for causal graphs with unobserved variables. Further, we perform experiments to show improvements over baselines in this setting.