A Conceptual Explanation of Bayesian Hyperparameter Optimization for Machine Learning

These figures compare validation error for hyperparameter optimization of an image classification neural network with random search in grey and Bayesian Optimization (using the Tree Parzen Estimator or TPE) in green. Lower is better: a smaller validation set error generally means better test set performance, and a smaller number of trials means less time invested. Clearly, there are significant advantages to Bayesian methods, and these graphs, along with other impressive results, convinced me it was time to take the next step and learn model-based hyperparameter optimization. The one-sentence summary of Bayesian hyperparameter optimization is: build a probability model of the objective function and use it to select the most promising hyperparameters to evaluate in the true objective function. If you like to operate at a very high level, then this sentence may be all you need. However, if you want to understand the details, this article is my attempt to outline the concepts behind Bayesian optimization, in particular Sequential Model-Based Optimization (SMBO) with the Tree Parzen Estimator (TPE).