Practical First-Order Bayesian Optimization Algorithms
Utkarsh Prakash Aryan Chollera Kushagra Khatwani Prabuchandran K. J. Tejas Bodas
First Order Bayesian Optimization (FOBO) is a sample efficient sequential
approach to find the global maxima of an expensive-to-evaluate black-box
objective function by suitably querying for the function and its gradient
evaluations. Such methods assume Gaussian process (GP) models for both, the
function and its gradient, and use them to construct an acquisition function
that identifies the next query point. In this paper, we propose a class of
practical FOBO algorithms that efficiently utilizes the information from the
gradient GP to identify potential query points with zero gradients. We
construct a multi-level acquisition function where in the first step, we
optimize a lower level acquisition function with multiple restarts to identify
potential query points with zero gradient value. We then use the upper level
acquisition function to rank these query points based on their function values
to potentially identify the global maxima. As a final step, the potential point
of maxima is chosen as the actual query point. We validate the performance of
our proposed algorithms on several test functions and show that our algorithms
outperform state-of-the-art FOBO algorithms. We also illustrate the application
of our algorithms in finding optimal set of hyper-parameters in machine
learning and in learning the optimal policy in reinforcement learning tasks.