Identifying Best Interventions through Online Importance Sampling
This addresses optimization challenges in computational advertising and systems biology, offering incremental improvements over existing bandit methods.
The paper tackles the problem of identifying the best soft interventions in a causal graph to maximize a target variable, given budget and cost constraints, by framing it as a best arm identification bandit problem. It provides improved error and regret bounds and shows empirical outperformance on datasets like Flow Cytometry and Inception-v3.
Motivated by applications in computational advertising and systems biology, we consider the problem of identifying the best out of several possible soft interventions at a source node $V$ in an acyclic causal directed graph, to maximize the expected value of a target node $Y$ (located downstream of $V$). Our setting imposes a fixed total budget for sampling under various interventions, along with cost constraints on different types of interventions. We pose this as a best arm identification bandit problem with $K$ arms where each arm is a soft intervention at $V,$ and leverage the information leakage among the arms to provide the first gap dependent error and simple regret bounds for this problem. Our results are a significant improvement over the traditional best arm identification results. We empirically show that our algorithms outperform the state of the art in the Flow Cytometry data-set, and also apply our algorithm for model interpretation of the Inception-v3 deep net that classifies images.