Lower Bounds on the Noiseless Worst-Case Complexity of Efficient Global Optimization.

Efficient global optimization is a widely used method for optimizing expensive black-box functions. In this paper, we study the worst-case oracle complexity of the efficient global optimization problem. In contrast to existing kernel-specific results, we derive a unified lower bound for the oracle complexity of efficient global optimization in terms of the metric entropy of a ball in its corresponding reproducing kernel Hilbert space. Moreover, we show that this lower bound nearly matches the upper bound attained by non-adaptive search algorithms, for the commonly used squared exponential kernel and the Matérn kernel with a large smoothness parameter ν. This matching is up to a replacement of d/2 by d and a logarithmic term logRϵ, where d is the dimension of input space, R is the upper bound for the norm of the unknown black-box function, and ϵ is the desired accuracy. That is to say, our lower bound is nearly optimal for these kernels.

Mapping the Insomnia Severity Index Instrument to EQ-5D Health State Utilities: A United Kingdom Perspective.

OBJECTIVE: This study aimed to map the Insomnia Severity Index (ISI) to the EQ-5D-3L utility values from a UK perspective. METHODS: Source data were derived from the 2020 National Health and Wellness Survey (NHWS) for France, Germany, Italy, Spain, the UK and the US. Ordinary least squares regression, generalised linear model (GLM), censored least absolute deviation, and adjusted limited dependent variable mixture model (ALDVMM) were employed to explore the relationship between ISI total summary score and EQ-5D utility while accounting for adjustment covariates derived from the NHWS. Fitting performance was assessed using standard metrics, including mean-squared error (MSE) and coefficient of determination (R2). RESULTS: A total of 17,955 respondent observations were included, with a mean ISI score of 12.12 ± 5.32 and a mean EQ-5D-3L utility (UK tariff) of 0.71 ± 0.23. GLM gamma-log and ALDVMM were the two best performing models. The ALDVMM had better fitting performance (R2 = 0.320, MSE 0.0347) than the GLM gamma-log (R2 = 0.303, MSE 0.0353); in train-test split-sample validation, ALDVMM also slightly outperformed the GLM gamma-log model, with an MSE of 0.0351 versus 0.0355. Based on fitting performance, ALDVMM and GLM gamma-log were the preferred models. CONCLUSIONS: In the absence of preference-based measures, this study provides an updated mapping algorithm for estimating EQ-5D-3L utilities from the ISI summary total score. This new mapping not only draws its strengths from the use of a large international dataset but also the incorporation of adjustment variables (including sociodemographic and general health characteristics) to reduce the effects of confounders.