Abstract
AbstractGlobal optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization
Reference43 articles.
1. Banjac, G., Stellato, B., Moehle, N., Goulart, P., Bemporad, A., Boyd, S.: Embedded code generation using the OSQP solver. In: Proc. 56th IEEE Conf. on Decision and Control, pp. 1906–1911, Melbourne, Australia, 2017. https://github.com/oxfordcontrol/osqp
2. Bemporad, A.: Model-based predictive control design: new trends and tools. In: Proc. 45th IEEE Conf. on Decision and Control, pp. 6678–6683, San Diego, CA (2006)
3. Bemporad, A.: A multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares. IEEE Trans. Autom. Control 60(11), 2892–2903 (2015)
4. Bemporad, A.: Global optimization via inverse distance weighting. 2019. Available on arXiv at arxiv:1906.06498. Code available at http://cse.lab.imtlucca.it/~bemporad/glis
5. Bemporad, A., Piga, D.: Active preference learning based on radial basis functions. 2019. Available on arXiv at arxiv:1909.13049. Code available at http://cse.lab.imtlucca.it/~bemporad/idwgopt
Cited by
35 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献