Abstract
Recent advances in many fields ranging from engineering to natural science, require increasingly complicated optimization tasks in the experiment design, for which the target objectives are generally in the form of black-box functions that are expensive to evaluate. In a common formulation of this problem, a designer is expected to solve the black-box optimization tasks via sequentially attempting candidate solutions and receiving feedback from the system. This thesis considers Bayesian optimization (BO) as the black-box optimization framework, and investigates the enhancements on BO from the aspects of efficiency, adaptation and reliability.Generally, BO consists of a surrogate model for providing probabilistic inference and an acquisition function which leverages the probabilistic inference for selecting the next candidate solution. Gaussian process (GP) is a prominent non-parametric surrogate model, and the quality of its inference is a critical factor on the optimality performance of BO. In many applications, the inherent randomness of the optimization problem caused by the environment conditions may lead to data distribution shift. To enable efficient and adaptive BO in auxiliary optimization tasks, i.e., reaching sub-optimal performance within limited attempts, transfer Bayesian meta-learning is adopted to generalize the surrogate model to address the data distribution shift.
Subsequently, the efficiency and adaptation of meta-learned BO is investigated on a simulated radio resource management (RRM) problem with discrete search space. While the regularity assumptions in GP hold only for continuous input space, this study also formulates the stochastic multi-armed bandit (MAB) model with Bayesian meta-learning for comparison. To further improve the efficiency and adaptation of both BO and MAB schemes, this study introduces a novel mechanism to configure optimizer models with knowledge transferred from graph-based contextual information built upon dynamic network topology.
Furthermore, this study covers the efficiency improvement of multi-fidelity BO (MFBO) with auxiliary optimization tasks addressed sequentially in a fully online manner. To mitigate the problem of evaluating costly objective functions, multi-fidelity optimization setting assumes the designer has access to approximations of the objective functions rather than directly evaluating true objectives, for which higher fidelity evaluations account for better approximations with larger costs. This work devises a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The knowledge transfer, represented by inter-task latent variables, is implemented via particle-based variational Bayesian updates.
Theoretical studies on reliability of BO in sequential black-box optimization with safety constraints on the search space are also covered in this work. The reliability refers to a formal guarantee that the designer is constrained to limit the number of unsafe solutions that are attempted throughout the optimization process in regardless of the assumptions on the surrogate model and evaluations noise level. Online conformal prediction (CP) is adopted in this study to calibrate the set of safe solutions provided by the surrogate model, and obtain the theoretical guarantee by allowing for an arbitrary, controllable but non-zero, rate of violation of the safety constraint. The proposed method is validated on both synthetic and real-world data.
| Date of Award | 1 Aug 2024 |
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| Original language | English |
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| Supervisor | Osvaldo Simeone (Supervisor) & Yansha Deng (Supervisor) |