Abstract

The predictive performance of a machine learning model highly depends on the corresponding hyper-parameter setting. Hence, hyper-parameter tuning is often indispensable. Normally such tuning requires the dedicated machine learning model to be trained and evaluated on centralized data to obtain a performance estimate. However, in a distributed machine learning scenario, it is not always possible to collect all the data from all nodes due to privacy concerns or storage limitations. Moreover, if data has to be transferred through low bandwidth connections it reduces the time available for tuning. Model-Based Optimization (MBO) is one state-of-the-art method for tuning hyper-parameters but the application on distributed machine learning models or federated learning lacks research. This work proposes a framework textit{MODES} that allows to deploy MBO on resource-constrained distributed embedded systems. Each node trains an individual model based on its local data. The goal is to optimize the combined prediction accuracy. The presented framework offers two optimization modes: (1) textit{MODES}-B considers the whole ensemble as a single black box and optimizes the hyper-parameters of each individual model jointly, and (2) textit{MODES}-I considers all models as clones of the same black box which allows it to efficiently parallelize the optimization in a distributed setting. We evaluate textit{MODES} by conducting experiments on the optimization for the hyper-parameters of a random forest and a multi-layer perceptron. The experimental results demonstrate that, with an improvement in terms of mean accuracy (textit{MODES}-B), run-time efficiency (textit{MODES}-I), and statistical stability for both modes, textit{MODES} outperforms the baseline, i.e., carry out tuning with MBO on each node individually with its local sub-data set.

Highlights

  • Nowadays, statistical and machine learning algorithms are used more frequently and intensively to solve problems in a wide range of applications, e.g., smart home, medical diagnosis, and environment analysis

  • We evaluated all combinations and report the accuracy of the classification results for two machine learning algorithms and three data splitting strategies separately for the different data sets

  • These results show that the B-EI outperforms all the other methods in most of the evaluated cases w.r.t. the mean prediction accuracy and/or statistical stability

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Summary

Introduction

Statistical and machine learning algorithms are used more frequently and intensively to solve problems in a wide range of applications, e.g., smart home, medical diagnosis, and environment analysis. The most direct and easy to implement tuning algorithm is grid search (LeCun et al 2012) which discretizes the hyper-parameter search space and exhaustively evaluates all possible combinations in a Cartesian grid to find the setting with the best performance. Another variation is random search (Bergstra and Bengio 2012), which randomly samples hyperparameter settings from the search space. Several extensions are proposed to speed up the BNN, e.g., sample multiple sub-networks from a network trained with Dropout (Srivastava et al 2014; Gal and Ghahramani 2016)

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