Confounded Budgeted Causal Bandits
This work addresses the challenge of efficient intervention selection in causal inference for applications like healthcare or marketing, though it is incremental by extending existing bandit methods to handle non-uniform costs and confounders.
The paper tackles the problem of learning optimal interventions under budget constraints and non-uniform costs in causal graphs with hidden confounders, proposing algorithms that achieve lower cumulative and simple regret than state-of-the-art methods, as shown in empirical evaluations.
We study the problem of learning 'good' interventions in a stochastic environment modeled by its underlying causal graph. Good interventions refer to interventions that maximize rewards. Specifically, we consider the setting of a pre-specified budget constraint, where interventions can have non-uniform costs. We show that this problem can be formulated as maximizing the expected reward for a stochastic multi-armed bandit with side information. We propose an algorithm to minimize the cumulative regret in general causal graphs. This algorithm trades off observations and interventions based on their costs to achieve the optimal reward. This algorithm generalizes the state-of-the-art methods by allowing non-uniform costs and hidden confounders in the causal graph. Furthermore, we develop an algorithm to minimize the simple regret in the budgeted setting with non-uniform costs and also general causal graphs. We provide theoretical guarantees, including both upper and lower bounds, as well as empirical evaluations of our algorithms. Our empirical results showcase that our algorithms outperform the state of the art.