Abstract. We consider the problem of optimizing a real-valued continuous function f , which is supposed to be expensive to evaluate and, consequently, can only be evaluated a limited number of times. This article focuses on the Bayesian approach to this problem, which consists in combining evaluation results and prior information about f in order to efficiently select new evaluation points, as long as the budget for evaluations is not exhausted. The algorithm called efficient global optimization (EGO), proposed by Jones, Schonlau and Welch (J. Global Optim., 13(4): 1998), is one of the most popular Bayesian optimization algorithms. It is based on a sampling criterion called the expected improvement (EI), which assumes a Gaussian process prior about f . In the EGO algorithm, the parameters of the covariance of the Gaussian process are estimated from the evaluation results by maximum likelihood, and these parameters are then plugged in the EI sampling criterion. However, it is well-known that this plug-in strategy can lead to very disappointing results when the evaluation results do not carry enough information about f to estimate the parameters in a satisfactory manner. We advocate a fully Bayesian approach to this problem, and derive an analytical expression for the EI criterion in the case of Student predictive distributions. Numerical experiments show that the fully Bayesian approach makes EI-based optimization more robust while maintaining an average loss similar to that of the EGO algorithm.
We consider the problem of optimizing a real-valued continuous function f using a Bayesian approach, where the evaluations of f are chosen sequentially by combining prior information about f , which is described by a random process model, and past evaluation results. The main difficulty with this approach is to be able to compute the posterior distributions of quantities of interest which are used to choose evaluation points. In this article, we decide to use a Sequential Monte Carlo (SMC) approach.
The conception of analog and mixed-signal functions requires great effort because the complex analog parts should be recursively optimized based not only on system-level requirements but also on technological limitations and imperfections. High-level behavioral models used for chip-level simulations can be employed using multi-domain hardware description languages (HDL), but they are usually manually written and lack technological characteristics. Moreover, automatic resizing and optimization at the transistor level are very limited, and the behavioral models cannot be readjusted to changes at the transistor level. In this paper, we present an efficient design methodology implying the automatic optimization of cells at the transistor level using a modified Bayesian Kriging approach and the extraction of robust analog macro-models, which can be directly regenerated during the optimization process. Coherent results were obtained when using the proposed methodology for the conception of a sixthorder continuous-time (CT) Sigma-Delta () modulator. I.
We apply the banded matrix inversion theorem given by Kavcic and Moura [1] to symmetric Toeplitz matrices. If the inverse is banded with bandwidth smaller than its size, there is a gain in arithmetic complexity compared to the current methods for Toeplitz matrix inversion. Our algorithm can also be used to find an approximation of the inverse matrix even though it is not exactly banded, but only well localized around its diagonal.
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