Many problems involve systems in which causal relationships among variables are represented by causal graphs. Because experimental data are often costly, learning procedures must combine statistical inference with sequential decision making. This dissertation develops methods for learning and inference of causal graphical models under sequential data collection, integrating observational and interventional information to support both optimal decision making and causal structure discovery. The analysis is conducted under linear structural equation models with Gaussian errors, which provide a direct link between causal effects and regression estimation.
The first part of the dissertation (Chapters 2 and 3) studies sequential identification of the intervention with the largest causal effect on a reward variable in an unknown graph. Interventions are treated as actions, and the objective is to determine which intervention produces the greatest effect on the reward. We develop upper-confidence-bound–based algorithms that exploit potential causal relationships among variables to improve learning efficiency relative to standard bandit methods. Under causal sufficiency, observational data are incorporated to construct valid confidence bounds for causal effects, leading to improved regret guarantees. The framework is then extended to settings with latent confounders, where some causal effects may not be identifiable through adjustment. The resulting method distinguishes identifiable and non-identifiable interventions and provides regret bounds that reflect this distinction. Theoretical analysis establishes finite-sample regret guarantees, and simulation studies demonstrate improved learning efficiency compared with existing methods.
The second part of the dissertation (Chapter 4) studies adaptive causal structure learning. Observational data determine a directed acyclic graph only up to its Markov equivalence class, and interventions are required to resolve the remaining uncertainty. We propose a sequential experimental design procedure that selects interventions based on uncertainty in edge orientation and updates the graph using statistical evidence. Theoretical analysis shows that the proposed procedure recovers the true graph almost surely, and numerical experiments demonstrate that it requires fewer interventions than sequential-random and complete-random baseline strategies.