  Modern machine learning algorithms usually involve tuning multiple (from one
to thousands) hyperparameters which play a pivotal role in terms of model
generalizability. Black-box optimization and gradient-based algorithms are two
dominant approaches to hyperparameter optimization while they have totally
distinct advantages. How to design a new hyperparameter optimization technique
inheriting all benefits from both approaches is still an open problem. To
address this challenging problem, in this paper, we propose a new
hyperparameter optimization method with zeroth-order hyper-gradients (HOZOG).
Specifically, we first exactly formulate hyperparameter optimization as an
A-based constrained optimization problem, where A is a black-box optimization
algorithm (such as deep neural network). Then, we use the average zeroth-order
hyper-gradients to update hyperparameters. We provide the feasibility analysis
of using HOZOG to achieve hyperparameter optimization. Finally, the
experimental results on three representative hyperparameter (the size is from 1
to 1250) optimization tasks demonstrate the benefits of HOZOG in terms of
simplicity, scalability, flexibility, effectiveness and efficiency compared
with the state-of-the-art hyperparameter optimization methods.

Machine Learning