Conceitos essenciais
Minimal Terminal Variance (MTV) is a batch design method that generates an initial batch by optimizing an acquisition function, and uses the same acquisition function to design all batches in a Batch Bayesian Optimization sequence.
Resumo
The content discusses Batch Bayesian Optimization (BBO), which is an effective but time-consuming method for measuring the quality of engineered systems at different settings. To reduce the total time required, experimenters may employ BBO, which is parsimonious with measurements, and take measurements of multiple settings simultaneously, in a batch.
The key insights are:
The initial batch in a BBO sequence is important yet under-studied. It contains a significant portion of the total number of measurements taken across all batches, due to the low budget. Also, since each subsequent, improvement-batch design will depend on the initialization measurements, better initialization will indirectly improve those designs.
The authors propose a batch design method called Minimal Terminal Variance (MTV), which generates an initial batch by optimizing an acquisition function. Further, they use the same acquisition function to design all batches in a BBO sequence.
MTV adapts a design criterion function from Design of Experiments, called I-Optimality, which minimizes the variance of the post-evaluation estimates of quality, integrated over the entire space of settings. MTV weights the integral by the probability that a setting is optimal, making it able to design not only an initial batch but all subsequent batches as well.
Numerical experiments on test functions and simulators show that MTV compares favorably to other BBO methods, and is the only method that (i) initializes BBO via optimization rather than random sampling, and (ii) may be effectively applied to both initialization and improvement batches.
Estatísticas
The content does not provide any specific numerical data or metrics to support the key claims. It focuses on describing the proposed MTV method and comparing its performance to other Batch Bayesian Optimization methods.
Citações
"The initial batch in a BBO sequence is important yet under-studied. It is important because the initial batch contains a significant portion of the total number measurements taken across all batches, due to the low budget."
"MTV adapts a design criterion function from Design of Experiments, called I-Optimality, which minimizes the variance of the post-evaluation estimates of quality, integrated over the entire space of settings. MTV weights the integral by the probability that a setting is optimal, making it able to design not only an initial batch but all subsequent batches as well."