Open Loop Hyperparameter Optimization and Determinantal Point Processes

Jesse Dodge, Kevin Jamieson, Noah A. Smith

Abstract:

Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.
In particular, we propose the use of $k$-determinantal point processes in hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity. We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over spaces with a mixture of discrete and continuous dimensions. Our experiments show significant benefits over uniform random search in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel.

TL;DR: Driven by the need for parallelizable, open-loop hyperparameter optimization methods, we propose the use of $k$-determinantal point processes in hyperparameter optimization via random search.

Keywords: hyperparameter optimization, random search, determinantal point processes, low discrepancy sequences