Online Experimental Design With Estimation-Regret Trade-off Under Network Interference

Network interference has attracted significant attention in the field of causal inference, encapsulating various sociological behaviors in which the treatment assigned to one individual within a network may affect the outcomes of others, such as their neighbors. A key challenge in this setting is that standard causal inference methods often assume independent treatment effects among individuals, which may not hold in networked environments. To estimate interference-aware causal effects, a traditional approach is to inherit the independent settings, where practitioners randomly assign experimental participants to different groups and compare their outcomes. Although effective in offline settings, this strategy becomes problematic in sequential experiments, where suboptimal decisions persist, leading to substantial regret. To address this issue, we introduce a unified interference-aware framework for online experimental design. Compared to existing studies, we extend the definition of arm space using the statistical concept of exposure mapping, which allows for a more flexible and context-aware representation of treatment effects in network settings. Crucially, we establish a Pareto-optimal trade-off between estimation accuracy and regret under the network concerning both time period and arm space, which remains superior to baseline models even without network interference. Furthermore, we propose an algorithmic implementation and discuss its generalization in different learning settings and network topology.