On the Trade-Off Between Number of Examples and Precision of Supervision in Regression

Gnecco, Giorgio; Nutarelli, Federico

doi:10.1007/978-3-030-16841-4_1

Cited by 8 publications

(2 citation statements)

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“…This possibility is particularly important when there are upper bounds on the available total computational time. It is worth mentioning that these arguments have been proved in [48] for the related problem of regression, whose investigation can be considered as a preliminary step for the analysis of surrogate optimization (indeed, it involves only the construction of the approximating function, but not its successive optimization). Possible choices for the iterative optimization algorithm, examined in this paper are: a) Method of Moving Asymptotes (MMA) [33] and its Globally Convergent upgrade (GCMMA) [34].…”

Section: Appendix C: Iterative Optimization Algorithmsmentioning

confidence: 92%

“…In that context, Quasi-Monte Carlo sequences are often preferred to realizations of Monte Carlo ones, because the former are typically able to cover the domain Ω in a more uniform way than the latter (see, e.g., [17] for an illustrative comparison). In other words, points generated from Quasi-Monte It is worth mentioning that these arguments have been proved in [48] for the related problem of regression, whose investigation can be considered as a preliminary step for the analysis of surrogate optimization (indeed, it involves only the construction of the approximating function, but not its successive optimization). Possible choices for the iterative optimization algorithm, examined in this paper are: a) Method of Moving Asymptotes (MMA) [33] and its Globally Convergent upgrade (GCMMA) [34].…”

Section: Appendix B: Surrogate Optimizationmentioning

confidence: 96%

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Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials

Bacigalupo

Gnecco

Lepidi

et al. 2019

J Optim Theory Appl

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Recently, an increasing research effort has been dedicated to analyse the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet-Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well-performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.

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Section: Appendix C: Iterative Optimization Algorithmsmentioning

confidence: 92%