Causal reasoning plays a central role in learning and decision-making in settings where distinguishing causal effect from spurious association is essential for valid prediction and action. However, many causal methods rely on strong assumptions, such as full observability, known causal structure, or independence across units. These assumptions are often violated in real-world applications. This thesis develops statistical and algorithmic foundations for causal learning and sequential decision-making, with a focus on identifiability, sample complexity, and structure-dependent regret bounds when classical assumptions are relaxed.

The first part of the thesis studies causal imitation learning in settings with latent variables and structural mismatch between experts and learners. We show that imitability is fundamentally a problem of causal identifiability rather than statistical consistency alone. We introduce context-specific independence relations and characterize when such structure enables imitation in settings that are otherwise non-imitable. We establish computational hardness results and derive graphical criteria for feasibility under mild structural assumptions. We also propose sound algorithmic approaches that integrate causal structure with observational data.

The second part focuses on the sample complexity of causal discovery for continuous variables. We study nonparametric conditional independence testing based on Von Mises expansions and kernel density estimation, and establish concentration inequalities and finite-sample guarantees under smoothness assumptions. These results yield explicit sample complexity bounds for constraint-based causal discovery in nonlinear and non-Gaussian settings. We further study distributional closeness testing between observational and interventional distributions. We show how such tests enable the identification of the causal direction in the presence of hidden confounding.

The final part addresses sequential decision-making problems with causal structure and interference. We study causal bandit models with heterogeneous intervention costs, hidden confounding, and derive regret bounds that quantify the benefits of combining observational and interventional data under general causal graphs. We then study bandit problems with network interference, including settings with unknown graphs, and design algorithms whose performance depends on graph structure rather than the size of the action space.

In summary, this thesis contributes theoretical results on causal imitation learning, causal discovery, and sequential decision-making, and characterizes fundamental limits and guarantees for learning and inference under structural constraints.