  Hyperparameter tuning is an active area of research in machine learning,
where the aim is to identify the optimal hyperparameters that provide the best
performance on the validation set. Hyperparameter tuning is often achieved
using naive techniques, such as random search and grid search. However, most of
these methods seldom lead to an optimal set of hyperparameters and often get
very expensive. In this paper, we propose a bilevel solution method for solving
the hyperparameter optimization problem that does not suffer from the drawbacks
of the earlier studies. The proposed method is general and can be easily
applied to any class of machine learning algorithms. The idea is based on the
approximation of the lower level optimal value function mapping, which is an
important mapping in bilevel optimization and helps in reducing the bilevel
problem to a single level constrained optimization task. The single-level
constrained optimization problem is solved using the augmented Lagrangian
method. We discuss the theory behind the proposed algorithm and perform
extensive computational study on two datasets that confirm the efficiency of
the proposed method. We perform a comparative study against grid search, random
search and Bayesian optimization techniques that shows that the proposed
algorithm is multiple times faster on problems with one or two hyperparameters.
The computational gain is expected to be significantly higher as the number of
hyperparameters increase. Corresponding to a given hyperparameter most of the
techniques in the literature often assume a unique optimal parameter set that
minimizes loss on the training set. Such an assumption is often violated by
deep learning architectures and the proposed method does not require any such
assumption.
