Derivative-Free Global Optimization Algorithms: Bayesian Method and Lipschitzian Approaches
This is an incremental survey paper that introduces existing derivative-free optimization methods for deep learning practitioners facing local optimum issues.
The paper tackles the problem of deep learning models getting stuck in local optima due to non-convex objective functions by introducing derivative-free global optimization algorithms, such as Bayesian methods and Lipschitzian approaches, to potentially improve training.
In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation algorithm, which updates the model variables layers by layers with the gradient descent algorithm or its variants. However, the objective functions of deep learning models to be optimized are usually non-convex and the gradient descent algorithms based on the first-order derivative can get stuck into the local optima very easily. To resolve such a problem, various local or global optimization algorithms have been proposed, which can help improve the training of deep learning models greatly. The representative examples include the Bayesian methods, Shubert-Piyavskii algorithm, Direct, LIPO, MCS, GA, SCE, DE, PSO, ES, CMA-ES, hill climbing and simulated annealing, etc. One part of these algorithms will be introduced in this paper (including the Bayesian method and Lipschitzian approaches, e.g., Shubert-Piyavskii algorithm, Direct, LIPO and MCS), and the remaining algorithms (including the population based optimization algorithms, e.g., GA, SCE, DE, PSO, ES and CMA-ES, and random search algorithms, e.g., hill climbing and simulated annealing) will be introduced in the follow-up paper [18] in detail.