Additive Causal Bandits with Unknown Graph
This work addresses the challenge of efficient intervention selection in causal inference for scenarios with unknown causal graphs, representing an incremental advance by introducing an additive assumption to overcome exponential hardness.
The paper tackles the problem of selecting optimal interventions in causal bandits without prior knowledge of the causal graph, assuming no latent confounders and an additive outcome structure. It proposes an action-elimination algorithm that achieves sample complexity bounds and empirically validates that explicit learning of the outcome's parents is unnecessary.
We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.