Hyperparameter Optimization: A Spectral Approach

TL;DR

This paper introduces a fast, spectral-based hyperparameter optimization algorithm that outperforms existing methods in speed and solution quality, with theoretical guarantees and applications to neural networks and decision trees.

Contribution

The paper presents a novel spectral approach to hyperparameter optimization using compressed sensing, providing both practical improvements and theoretical guarantees.

Findings

Significantly better solutions than Hyperband and Spearmint

At least 10x faster than Hyperband and Bayesian Optimization

First quasi-polynomial time algorithm for learning noisy decision trees

Abstract

We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large number of hyperparameters. The algorithm --- an iterative application of compressed sensing techniques for orthogonal polynomials --- requires only uniform sampling of the hyperparameters and is thus easily parallelizable. Experiments for training deep neural networks on Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband and Spearmint), our algorithm finds significantly improved solutions, in some cases better than what is attainable by hand-tuning. In terms of overall running time (i.e., time required to sample various settings of hyperparameters plus additional computation time), we are at least an order of magnitude faster than Hyperband and Bayesian Optimization. We also outperform Random Search 8x. Additionally, our method comes with provable guarantees and yields the first improvements on the sample complexity of learning decision trees in over two decades. In particular, we obtain the first quasi-polynomial time algorithm for learning noisy decision trees with polynomial sample complexity.