Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates

The optimization of algorithm (hyper-)parameters is crucial for achieving peak performance across a wide range of domains, ranging from deep neural networks to solvers for hard combinatorial problems. The resulting algorithm configuration (AC) problem has attracted much attention from the machine learning community. However, the proper evaluation of new AC procedures is hindered by two key hurdles. First, AC benchmarks are hard to set up. Second and even more significantly, they are computationally expensive: a single run of an AC procedure involves many costly runs of the target algorithm whose performance is to be optimized in a given AC benchmark scenario. One common workaround is to optimize cheap-to-evaluate artificial benchmark functions (e.g., Branin) instead of actual algorithms; however, these have different properties than realistic AC problems. Here, we propose an alternative benchmarking approach that is similarly cheap to evaluate but much closer to the original AC problem: replacing expensive benchmarks by surrogate benchmarks constructed from AC benchmarks. These surrogate benchmarks approximate the response surface corresponding to true target algorithm performance using a regression model, and the original and surrogate benchmark share the same (hyper-)parameter space. In our experiments, we construct and evaluate surrogate benchmarks for hyperparameter optimization as well as for AC problems that involve performance optimization of solvers for hard combinatorial problems, drawing training data from the runs of existing AC procedures. We show that our surrogate benchmarks capture overall important characteristics of the AC scenarios, such as high- and low-performing regions, from which they were derived, while being much easier to use and orders of magnitude cheaper to evaluate

Hyperparameters, tuning and meta-learning for random forest and other machine learning algorithms

In this cumulative dissertation thesis, I examine the influence of hyperparameters on machine learning algorithms, with a special focus on random forest. It mainly consists of three papers that were written in the last three years. The first paper (Probst and Boulesteix, 2018) examines the influence of the number of trees on the performance of a random forest. In general it is believed that the number of trees should be set higher to achieve better performance. However, we show some real data examples in which the expectation of measures such as accuracy and AUC (partially) decrease with growing numbers of trees. We prove theoretically why this can happen and argue that this only happens in very special data situations. For other measures such as the Brier score, the logarithmic loss or the mean squared error, we show that this cannot happen. In a benchmark study based on 306 classification and regression datasets, we illustrate the extent of this unexpected behaviour. We observe that, on average, most of the improvement regarding performance can be achieved while growing the first 100 trees. We use our new OOBCurve R package (Probst, 2017a) for the analysis, which can be used to examine performances for a growing number of trees of a random forest based on the out-of-bag observations. The second paper (Probst et al., 2019b) is a more general work. Firstly we review literature about the influence of hyperparameters on random forest. The different hyperparameters considered are the number of variables drawn at each split, the sampling scheme for drawing observations for each tree, the minimum number of observations in a node that a tree is allowed to have, the number of trees and the splitting rule. Their influence is examined regarding performance, runtime and variable importance. In the second part of the paper different tuning strategies for obtaining optimal hyperparameters are presented. A new software package in R is introduced, tuneRanger. It executes the tuning strategy sequential model-based optimization based on the out-of-bag observations. The hyperparameters and ranges for tuning are chosen automatically. In a benchmark study this implementation is compared with other different implementations that execute tuning for random forest. The third paper (Probst et al., 2019a) is even more general and presents a general framework for examining the tunability of hyperparameters of machine learning algorithms. It first defines the concept of defaults properly and proposes definitions for measuring the tunability of the whole algorithm, of single hyperparameters and of combinations of hyperparameters. To apply these definitions to a collection of 38 binary classification datasets, a random bot is created, which generated in total around 5 million experiment runs of 6 algorithms with different hyperparameters. The details of this bot are described in an extra paper (Kühn et al., 2018), co-authored by myself, that is also included in this dissertation. The results of this bot are used to estimate the tunability of these 6 algorithms and their specific hyperparameters. Furthermore, ranges for parameter tuning of these algorithms are proposed