  This PhD thesis covers breakthroughs in several areas of adaptive experiment
design: (i) (Chapter 2) Novel clinical trial designs and statistical methods in
the era of precision medicine. (ii) (Chapter 3) Multi-armed bandit theory, with
applications to learning healthcare systems and clinical trials. (iii) (Chapter
4) Bandit and covariate processes, with finite and non-denumerable set of arms.
(iv) (Chapter 5) A rigorous framework for simulation-based verification of
adaptive design properties.
