AI-assisted decision-making systems have revolutionized fields ranging from medical treatment to online marketing by learning from data to optimize sequential decisions. However, real-world deployment reveals fundamental challenges that compromise system reliability and effectiveness. For instance, human users may distrust or selectively follow algorithmic recommendations, creating implementation gaps; operating environments often differ frequently from the conditions under which systems were trained; and complete knowledge about the environment is often unavailable. Existing methods typically assume perfect implementation and stable environments, leading to substantial performance degradation when these assumptions fail. This project aims to address these limitations by developing new theories and principled algorithms to enable robust and trustworthy decision-making under realistic constraints. In addition, it will provide valuable opportunities for training students at all levels in the STEM field and introducing the general audience to advances in data science and AI. This project focuses on fundamental sequential decision-making problems: multi-armed bandit and reinforcement learning. The research pursues three complementary directions, aiming to characterize the fundamental statistical limits of learning and develop provably optimal algorithms while maintaining robustness to varied sources of uncertainties. The first thrust will devise trust-aware procedures that acc