Initial Design Strategies and their Effects on Sequential Model-Based Optimization
This work addresses the understudied choice of initial sampling in SMBO, which is incremental but important for optimizing expensive functions in fields like engineering and machine learning.
The paper investigates how the size and distribution of initial samples affect the performance of the EGO algorithm in sequential model-based optimization, finding that small initial budgets with Halton sampling are generally preferable but performance is unstructured and EGO sometimes underperforms random sampling.
Sequential model-based optimization (SMBO) approaches are algorithms for solving problems that require computationally or otherwise expensive function evaluations. The key design principle of SMBO is a substitution of the true objective function by a surrogate, which is used to propose the point(s) to be evaluated next. SMBO algorithms are intrinsically modular, leaving the user with many important design choices. Significant research efforts go into understanding which settings perform best for which type of problems. Most works, however, focus on the choice of the model, the acquisition function, and the strategy used to optimize the latter. The choice of the initial sampling strategy, however, receives much less attention. Not surprisingly, quite diverging recommendations can be found in the literature. We analyze in this work how the size and the distribution of the initial sample influences the overall quality of the efficient global optimization~(EGO) algorithm, a well-known SMBO approach. While, overall, small initial budgets using Halton sampling seem preferable, we also observe that the performance landscape is rather unstructured. We furthermore identify several situations in which EGO performs unfavorably against random sampling. Both observations indicate that an adaptive SMBO design could be beneficial, making SMBO an interesting test-bed for automated algorithm design.