This thesis presents work conducted in the domain of sequential decision-making in general and Bandit problems in particular, tackling challenges from a practical and theoretical perspective, framed in the contexts of mobile Health. The early stages of this work have been conducted in the context of the project ``improving Medication Adherence through Person-Centred Care and Adaptive Interventions'' (iMedA) which aims to provide personalized adaptive interventions to hypertensive patients, supporting them in managing their medication regimen. The focus lies on inadequate medication adherence (MA), a pervasive issue where patients do not take their medication as instructed by their physician. The selection of individuals for intervention through secondary database analysis on Electronic Health Records (EHRs) was a key challenge and is addressed through in-depth analysis of common adherence measures, development of prediction models for MA, and discussions on limitations of such approaches for analyzing MA. Providing personalized adaptive interventions is framed in several bandit settings and addresses the challenge of delivering relevant interventions in environments where contextual information is unreliable and full of noise. Furthermore, the need for good initial policies is explored and improved in the latent-bandits setting, utilizing prior collected data to optimal selection the best intervention at every decision point. As the final concluding work, this thesis elaborates on the need for privacy and explores different privatization techniques in the form of noise-additive strategies using a realistic recommendation scenario.         

The contributions of the thesis can be summarised as follows: (1) Highlighting the issues encountered in measuring MA through secondary database analysis and providing recommendations to address these issues, (2) Investigating machine learning models developed using EHRs for MA prediction and extraction of common refilling patterns through EHRs, (3) formal problem definition for a novel contextual bandit setting with context uncertainty commonly encountered in Mobile Health and development of an algorithm designed for such environments. (4) Algorithmic improvements, equipping the agent with information-gathering capabilities for active action selection in the latent bandit setting, and (5) exploring important privacy aspects using a realistic recommender scenario.