<p dir="ltr">Bandit and optimization represent prominent areas of machine learning research. Despite extensive prior research on these topics in various contexts, modern challenges, such as deal- ing with highly unsmooth nonlinear reward objectives and incorporating federated learning, have sparked new discussions. The X-armed bandit problem is a specialized case where bandit algorithms and blackbox optimization techniques join forces to address noisy reward functions within continuous domains to minize the regret. This thesis concentrates on the X -armed bandit problem in a modern setting. In the first chapter, we introduce an optimal statistical collaboration framework for the single-client X -armed bandit problem, expanding the range of objectives by considering more general smoothness assumptions and empha- sizing tighter statistical error measures to expedite learning. The second chapter addresses the federated X-armed bandit problem, providing a solution for collaboratively optimizing the average global objective while ensuring client privacy. In the third chapter, we confront the more intricate personalized federated X -armed bandit problem. An enhanced algorithm facilitating the simultaneous optimization of all local objectives is proposed.</p>

Optimization is omnipresent in our world. Its numerous applications spread from industrial cases, such as logistics, construction management or production planning; to the private sphere, filled with problems of selecting daycare or vacation planning. In this thesis, we concentrate on expensive black-box optimization (EBBO) problems, a subset of optimization problems (OPs), which are characterized by an expensive cost of evaluating an objective function. Such OPs are reoccurring in various domains, being known as: hyperpameter optimization in machine learning, performance configuration optimization or parameter tuning in search-based software engineering, simulation optimization in operations research, meta-optimization or parameter tuning in the optimization domain itself. High diversity of domains introduces a plethora of solving approaches, which adhere to a similar structure and workflow, but differ in details. The software frameworks stemming from different areas possess only partially intersecting manageability points, i.e., lack manageability. In this thesis, we argue that the lack of manageability in EBBO is a major problem, which leads to underachieving optimization quality. The goal of this thesis is to study the role of manageability in EBBO and to investigate whether improving the manageability of EBBO frameworks increases optimization quality. To reach this goal, we appeal to software product line engineering (SPLE), a methodology for developing highly-manageable software systems. Based on the foundations of SPLE, we introduce a novel framework for EBBO called BRISE. It offers: 1) a loosely-coupled software architecture, separating concerns of the experiment designer and the developer of EBBO strategies; 2) a full coverage of all EBBO problem types; and 3) a context-aware variability model, which captures the experiment-designer-defined OP with the content model; and manageability points including their variants and constraints with the cardinality-based feature model. High manageability of the introduced BRISE framework enables us: 1) to extend the framework with novel efficient strategies, such as adaptive repetition management; and 2) to introduce novel EBBO mechanisms, such as multi-objective compositional surrogate modeling, dynamic sampling and hierarchical surrogate modeling. The evaluation of the novel approaches with a set of case studies, including: the WFG benchmark for multi-objective optimization, combined selection and parameter control of meta-heuristics, and energy optimization; demonstrated their superiority over the state-of-the-art competitors. Thus, it supports the research hypothesis of this thesis: Improving manageability of an EBBO framework enables to increase optimization quality.