Bayesian Optimization for Hyper-Parameter

In past several weeks, I spent a tremendous amount of time on reading literature about automatic parameter tuning in the context of Machine Learning (ML), most of which can be classified into two major categories, e.g. search and optimization. Searching mechanisms, such as grid search, random search, and Sobol sequence, can be somewhat computationally expensive. However, they are extremely easy to implement and parallelize on a multi-core PC, as shown in https://statcompute.wordpress.com/2019/02/03/sobol-sequence-vs-uniform-random-in-hyper-parameter-optimization. On the other hand, optimization algorithms, especially gradient-free optimizers such as Nelder–Mead simplex and particle swarm, are often able to quickly locate close-to-optimal solutions in cases that the global optimal is neither feasible nor necessary, as shown in https://statcompute.wordpress.com/2019/02/10/direct-optimization-of-hyper-parameter and https://statcompute.wordpress.com/2019/02/23/gradient-free-optimization-for-glmnet-parameters.

In the example below, another interesting approach, namely Bayesian optimization (https://arxiv.org/abs/1206.2944), is demonstrated and compared with CMA-ES (https://www.researchgate.net/publication/227050324_The_CMA_Evolution_Strategy_A_Comparing_Review), which is also a popular gradient-free optimizer based on the evolution strategy. As shown in the result, the output from Bayesian optimization is closer to the one from Nelder–Mead simplex and particle swarm. What’s more, Bayesian optimization is more consistent than CMA-ES among multiple trials in the experiment.

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