Federated Combinatorial Causal Bandits with Heterogeneous Causal Influences

We explore the problem of federated combinatorial causal bandits (FedCCB), where multiple agents collaboratively select variables for intervention and gather feedback. The primary objective of FedCCB is to identify optimal interventions for each agent while minimizing the total cumulative regret associated with the target nodes. A key challenge in FedCCB stems from the inherent heterogeneity of local causal models, which often exhibit diverse causal influences. To address this challenge, we propose a novel Federated Subset-Clustered Bandit (FedSCuB) method. This method groups agents to tackle heterogeneity based on the similarity of their causal relationships with specified subsets of variables. FedSCuB incorporates an intervention-based exploration strategy to collect partial observations necessary for clustering, as well as an alternating minimization method to facilitate collaboration among agents within the same cluster. Theoretical analysis demonstrates that the proposed FedSCuB method achieves sub-linear regret and offers a better regret bound compared to baseline methods. Empirical evaluations on synthetic tasks further confirm the effectiveness and superiority of our method.