  This thesis rigorously studies fundamental reinforcement learning (RL)
methods in modern practical considerations, including robust RL, distributional
RL, and offline RL with neural function approximation. The thesis first
prepares the readers with an overall overview of RL and key technical
background in statistics and optimization. In each of the settings, the thesis
motivates the problems to be studied, reviews the current literature, provides
computationally efficient algorithms with provable efficiency guarantees, and
concludes with future research directions. The thesis makes fundamental
contributions to the three settings above, both algorithmically, theoretically,
and empirically, while staying relevant to practical considerations.
