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On the use of metaheuristics in hyperparameters optimization of gaussian processes

Due to difficulties such as multiple local optima and flat landscape, it is suggested to use global optimization techniques to discover the global optimum of the auxiliary optimization problem of finding good Gaussian Processes (GP) hyperparameters. We investigated the performance of genetic algorithms (GA), particle swarm optimization (PSO), differential evolution (DE), and covariance matrix adaptation evolution strategy (CMA-ES) for optimizing hyperparameters of GP. The study was performed on two artificial problems and also one real-world problem. From the results, we observe that PSO, CMA-ES, and DE/local-to-best/1 consistently outperformed two variants of GA and DE/rand/1 with per-generation-dither on all problems. In particular, CMA-ES is an attractive method since it is quasi-parameter free and it also demonstrates good exploitative and explorative power on optimizing the hyperparameters.