We present a new method for searching optimal hyperparameters among several tasks and several criteria. Multi-Task Multi Criteria method (MTMC) provides several Pareto-optimal solutions, among which one solution is selected with given criteria significance coefficients. The article begins with a mathematical formulation of the problem of choosing optimal hyperparameters. Then, the steps of the MTMC method that solves this problem are described. The proposed method is evaluated on the image classification problem using a convolutional neural network. The article presents optimal hyperparameters for various criteria significance coefficients.
With online professional network platforms (OPNs, e.g., LinkedIn, Xing, etc.) becoming popular on the web, people are now turning to these platforms to create and share their professional profiles, to connect with others who share similar professional aspirations and to explore new career opportunities. These platforms however do not offer a long-term roadmap to guide career progression and improve workforce employability. The career trajectories of OPN users can serve as a reference but they are not always optimal. A career plan can also be devised through consultation with career coaches, wh…
Deep learning models are full of hyperparameters, which are set manually before the learning process can start. To find the best configuration for these hyperparameters in such a high dimensional space, with time-consuming and expensive model training / validation, is not a trivial challenge. Bayesian optimization is a powerful tool for the joint optimization of hyperparameters, efficiently trading off exploration and exploitation of the hyperparameter space. In this paper, we discuss Bayesian hyperparameter optimization, including hyperparameter optimization, Bayesian optimization, and Gaussi…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact be…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as monotonic functions of the hyperparameters. Our proposed algorithm adapts Bayesian optimization methods to incorporate the monotonicity constraints. We illustrate the advantages of exploiting monotonicity using illustrative examples and demonstrate the improvements in optimization ef…
Institute of Computing Technology, CAS（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；WiseUranium corp.（WiseUranium公司）
Automl is the key technology for machine learning problem. Current state of art hyperparameter optimization methods are based on traditional black-box optimization methods like SMBO (SMAC, TPE). The objective function of black-box optimization is non-smooth, or time-consuming to evaluate, or in some way noisy. Recent years, many researchers offered the work about the properties of hyperparameters. However, traditional hyperparameter optimization methods do not take those information into consideration. In this paper, we use gradient information and machine learning model analysis information t…
We propose a new algorithm for hyperparameter selection in machine learning algorithms. The algorithm is a novel modification of Harmonica, a spectral hyperparameter selection approach using sparse recovery methods. In particular, we show that a special encoding of hyperparameter space enables a natural group-sparse recovery formulation, which when coupled with HyperBand (a multi-armed bandit strategy) leads to improvement over existing hyperparameter optimization methods such as Successive Halving and Random Search. Experimental results on image datasets such as CIFAR-10 confirm the benefits …
Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure. These gradients allow us to optimize thousands of hyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures. We compute hyperparameter gradients by exactly reversing the dynamics of stochastic gradient descent with mo…
Due to the high computational demands executing a rigorous comparison between hyperparameter optimization (HPO) methods is often cumbersome. The goal of this paper is to facilitate a better empirical evaluation of HPO methods by providing benchmarks that are cheap to evaluate, but still represent realistic use cases. We believe these benchmarks provide an easy and efficient way to conduct reproducible experiments for neural hyperparameter search. Our benchmarks consist of a large grid of configurations of a feed forward neural network on four different regression datasets including architectur…
Leibniz University Hannover（莱布尼茨汉诺威大学）；University of Freiburg（弗莱堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Algorithm parameters, in particular hyperparameters of machine learning algorithms, can substantially impact their performance. To support users in determining well-performing hyperparameter configurations for their algorithms, datasets and applications at hand, SMAC3 offers a robust and flexible framework for Bayesian Optimization, which can improve performance within a few evaluations. It offers several facades and pre-sets for typical use cases, such as optimizing hyperparameters, solving low dimensional continuous (artificial) global optimization problems and configuring algorithms to perf…
Harbin Institute of Technology（哈尔滨工业大学）；University of California San Diego（加州大学圣迭戈分校）
Machine learning algorithms are very sensitive to the hyperparameters, and their evaluations are generally expensive. Users desperately need intelligent methods to quickly optimize hyperparameter settings according to known evaluation information, and thus reduce computational cost and promote optimization efficiency. Motivated by this, we propose ExperienceThinking algorithm to quickly find the best possible hyperparameter configuration of machine learning algorithms within a few configuration evaluations. ExperienceThinking design two novel methods, which intelligently infer optimal configur…
A typical assumption in supervised machine learning is that the train (source) and test (target) datasets follow completely the same distribution. This assumption is, however, often violated in uncertain real-world applications, which motivates the study of learning under covariate shift. In this setting, the naive use of adaptive hyperparameter optimization methods such as Bayesian optimization does not work as desired since it does not address the distributional shift among different datasets. In this work, we consider a novel hyperparameter optimization problem under the multi-source covari…
This research proposes to use the Moreau-Yosida envelope to stabilize the convergence behavior of bi-level Hyperparameter optimization solvers, and introduces the new algorithm called Moreau-Yosida regularized Hyperparameter Optimization (MY-HPO) algorithm. Theoretical analysis on the correctness of the MY-HPO solution and initial convergence analysis is also provided. Our empirical results show significant improvement in loss values for a fixed computation budget, compared to the state-of-art bi-level HPO solvers.
Hyperparameters play a critical role in the performances of many machine learning methods. Determining their best settings or Hyperparameter Optimization (HPO) faces difficulties presented by the large number of hyperparameters as well as the excessive training time. In this paper, we develop an effective approach to reducing the total amount of required training time for HPO. In the initialization, the nested Latin hypercube design is used to select hyperparameter configurations for two types of training, which are, respectively, heavy training and light training. We propose a truncated addit…
We introduce an improved version of Random Search (RS), used here for hyperparameter optimization of machine learning algorithms. Unlike the standard RS, which generates for each trial new values for all hyperparameters, we generate new values for each hyperparameter with a probability of change. The intuition behind our approach is that a value that already triggered a good result is a good candidate for the next step, and should be tested in new combinations of hyperparameter values. Within the same computational budget, our method yields better results than the standard RS. Our theoretical …
In this paper we develop a Bayesian optimization based hyperparameter tuning framework inspired by statistical learning theory for classifiers. We utilize two key facts from PAC learning theory; the generalization bound will be higher for a small subset of data compared to the whole, and the highest accuracy for a small subset of data can be achieved with a simple model. We initially tune the hyperparameters on a small subset of training data using Bayesian optimization. While tuning the hyperparameters on the whole training data, we leverage the insights from the learning theory to seek more …
Nearly all model algorithms used in machine learning use two different sets of parameters: the training parameters and the meta-parameters (hyperparameters). While the training parameters are learned during the training phase, the values of the hyperparameters have to be specified before learning starts. For a given dataset, we would like to find the optimal combination of hyperparameter values, in a reasonable amount of time. This is a challenging task because of its computational complexity. In previous work [11], we introduced the Weighted Random Search (WRS) method, a combination of Random…
The performance of deep neural networks crucially depends on good hyperparameter configurations. Bayesian optimization is a powerful framework for optimizing the hyperparameters of DNNs. These methods need sufficient evaluation data to approximate and minimize the validation error function of hyperparameters. However, the expensive evaluation cost of DNNs leads to very few evaluation data within a limited time, which greatly reduces the efficiency of Bayesian optimization. Besides, the previous researches focus on using the complete evaluation data to conduct Bayesian optimization, and ignore …
Hyperparameter tuning is an omnipresent problem in machine learning as it is an integral aspect of obtaining the state-of-the-art performance for any model. Most often, hyperparameters are optimized just by training a model on a grid of possible hyperparameter values and taking the one that performs best on a validation sample (grid search). More recently, methods have been introduced that build a so-called surrogate model that predicts the validation loss for a specific hyperparameter setting, model and dataset and then sequentially select the next hyperparameter to test, based on a heuristic…
Pohang University of Science and Technology（浦项科技大学）；AITRICS
Hyperparameter optimization aims to find the optimal hyperparameter configuration of a machine learning model, which provides the best performance on a validation dataset. Manual search usually leads to get stuck in a local hyperparameter configuration, and heavily depends on human intuition and experience. A simple alternative of manual search is random/grid search on a space of hyperparameters, which still undergoes extensive evaluations of validation errors in order to find its best configuration. Bayesian optimization that is a global optimization method for black-box functions is now popu…
University of California, Irvine（加州大学欧文分校）；University of Hawai’i at Mãnoa（夏威夷大学马诺阿分校）
Sherpa is a hyperparameter optimization library for machine learning models. It is specifically designed for problems with computationally expensive, iterative function evaluations, such as the hyperparameter tuning of deep neural networks. With Sherpa, scientists can quickly optimize hyperparameters using a variety of powerful and interchangeable algorithms. Sherpa can be run on either a single machine or in parallel on a cluster. Finally, an interactive dashboard enables users to view the progress of models as they are trained, cancel trials, and explore which hyperparameter combinations are…
D.E. Shaw Research（D.E. Shaw 研究所）；Department of Biochemistry and Molecular Biophysics, Columbia University（哥伦比亚大学生物化学与分子生物物理学系）
Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently developed optimization methods can be used to select thousands or even millions of hyperparameters. Such methods often yield overfit models, however, leading to poor performance on unseen data. We argue that this overfitting results from using the standard hyperparameter optimization objective function. Here we present an alternative objective that is equivalent to…
Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and bandit-based methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configuratio…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Google Research（谷歌研究院）；Determined AI
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theo…
Bayesian Optimization is a popular tool for tuning algorithms in automatic machine learning (AutoML) systems. Current state-of-the-art methods leverage Random Forests or Gaussian processes to build a surrogate model that predicts algorithm performance given a certain set of hyperparameter settings. In this paper, we propose a new surrogate model based on gradient boosting, where we use quantile regression to provide optimistic estimates of the performance of an unobserved hyperparameter setting, and combine this with a distance metric between unobserved and observed hyperparameter settings to …
ETH Zurich（苏黎世联邦理工学院）；University of Toronto（多伦多大学）
Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance. This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima. In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters. During optimization we…
Indian Institute of Management Ahmedabad（印度管理学院艾哈迈达巴德分校）
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive techniques, such as random search and grid search. However, most of these methods seldom lead to an optimal set of hyperparameters and often get very expensive. In this paper, we propose a bilevel solution method for solving the hyperparameter optimization problem that does not suffer from the drawbacks of the earlier studies. The proposed method is general a…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）
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 des…
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best-arm identification framework has only been considered in the stochastic setting. We introduce the non-stochastic setting under this framework, identify a known algorithm that is well-suited for this setting, and analyze its behavior. Next, by leveraging the iterative nature of s…
We consider a class of a nested optimization problems involving inner and outer objectives. We observe that by taking into explicit account the optimization dynamics for the inner objective it is possible to derive a general framework that unifies gradient-based hyperparameter optimization and meta-learning (or learning-to-learn). Depending on the specific setting, the variables of the outer objective take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We show that some recently proposed methods in the latter setting can be instantiated …
The increasing demand for democratizing machine learning algorithms calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters which can cause a large variation in the training cost. But this effect is largely ignored in existing HPO methods, which are incapable to properly control cost during the optimization process. To address this problem, we develop a new cost-frugal HPO solution. The core of our solution is a simple but new randomized direct-search method, for which we prove a convergence rate of $O(\frac{\sqrt{d}}{\sqrt{K}})$…
Machine learning algorithms such as random forests or xgboost are gaining more importance and are increasingly incorporated into production processes in order to enable comprehensive digitization and, if possible, automation of processes. Hyperparameters of these algorithms used have to be set appropriately, which can be referred to as hyperparameter tuning or optimization. Based on the concept of tunability, this article presents an overview of theoretical and practical results for popular machine learning algorithms. This overview is accompanied by an experimental analysis of 30 hyperparamet…
Most machine learning algorithms are configured by one or several hyperparameters that must be carefully chosen and often considerably impact performance. To avoid a time consuming and unreproducible manual trial-and-error process to find well-performing hyperparameter configurations, various automatic hyperparameter optimization (HPO) methods, e.g., based on resampling error estimation for supervised machine learning, can be employed. After introducing HPO from a general perspective, this paper reviews important HPO methods such as grid or random search, evolutionary algorithms, Bayesian opti…
We present TaskSet, a dataset of tasks for use in training and evaluating optimizers. TaskSet is unique in its size and diversity, containing over a thousand tasks ranging from image classification with fully connected or convolutional neural networks, to variational autoencoders, to non-volume preserving flows on a variety of datasets. As an example application of such a dataset we explore meta-learning an ordered list of hyperparameters to try sequentially. By learning this hyperparameter list from data generated using TaskSet we achieve large speedups in sample efficiency over random search…
When developing and analyzing new hyperparameter optimization methods, it is vital to empirically evaluate and compare them on well-curated benchmark suites. In this work, we propose a new set of challenging and relevant benchmark problems motivated by desirable properties and requirements for such benchmarks. Our new surrogate-based benchmark collection consists of 14 scenarios that in total constitute over 700 multi-fidelity hyperparameter optimization problems, which all enable multi-objective hyperparameter optimization. Furthermore, we empirically compare surrogate-based benchmarks to the…
Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview
Fraunhofer Institut für integrierte Schaltungen（弗劳恩霍夫集成电路研究所）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Technische Universität Dortmund（多特蒙德工业大学）；Universidad Pontificia Comillas（康普卢滕塞大学）；Warwick Business School（华威商学院）
Tackling new machine learning problems with neural networks always means optimizing numerous hyperparameters that define their structure and strongly impact their performances. In this work, we study the use of goal-oriented sensitivity analysis, based on the Hilbert-Schmidt Independence Criterion (HSIC), for hyperparameter analysis and optimization. Hyperparameters live in spaces that are often complex and awkward. They can be of different natures (categorical, discrete, boolean, continuous), interact, and have inter-dependencies. All this makes it non-trivial to perform classical sensitivity…
Istituto Italiano di Tecnologia（意大利理工学院）；University College London（伦敦大学学院）；Università degli Studi di Firenze（佛罗伦萨大学）
We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the optimization dynamics for the inner objective. Depending on the specific setting, the outer variables take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We provide sufficient conditions under which solutions of the approximate problem converge to those of the exact problem. We instantiate our approach f…
Department of Computer Science, University of Toronto（多伦多大学计算机科学系）
Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and hyperparameters. Our process trains a neural network to output approximately optimal weights as a function of hyperparameters. We show that our technique converges to locally optimal weights and hyperparameters for sufficiently large hypernetworks. We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning tho…
Convolutional Neural Network is known as ConvNet have been extensively used in many complex machine learning tasks. However, hyperparameters optimization is one of a crucial step in developing ConvNet architectures, since the accuracy and performance are reliant on the hyperparameters. This multilayered architecture parameterized by a set of hyperparameters such as the number of convolutional layers, number of fully connected dense layers & neurons, the probability of dropout implementation, learning rate. Hence the searching the hyperparameter over the hyperparameter space are highly difficul…
Reinforcement learning algorithms can show strong variation in performance between training runs with different random seeds. In this paper we explore how this affects hyperparameter optimization when the goal is to find hyperparameter settings that perform well across random seeds. In particular, we benchmark whether it is better to explore a large quantity of hyperparameter settings via pruning of bad performers, or if it is better to aim for quality of collected results by using repetitions. For this we consider the Successive Halving, Random Search, and Bayesian Optimization algorithms, th…
Conventional hyperparameter optimization methods are computationally intensive and hard to generalize to scenarios that require dynamically adapting hyperparameters, such as life-long learning. Here, we propose an online hyperparameter optimization algorithm that is asymptotically exact and computationally tractable, both theoretically and practically. Our framework takes advantage of the analogy between hyperparameter optimization and parameter learning in recurrent neural networks (RNNs). It adapts a well-studied family of online learning algorithms for RNNs to tune hyperparameters and netwo…
JD Finance America Corporation（京东金融美国公司）；University of Pittsburgh（匹兹堡大学）；Nanjing University of Information Science & Technology（南京信息工程大学）
Modern machine learning algorithms usually involve tuning multiple (from one to thousands) hyperparameters which play a pivotal role in terms of model generalizability. Black-box optimization and gradient-based algorithms are two dominant approaches to hyperparameter optimization while they have totally distinct advantages. How to design a new hyperparameter optimization technique inheriting all benefits from both approaches is still an open problem. To address this challenging problem, in this paper, we propose a new hyperparameter optimization method with zeroth-order hyper-gradients (HOZOG)…
Automatically searching for optimal hyperparameter configurations is of crucial importance for applying deep learning algorithms in practice. Recently, Bayesian optimization has been proposed for optimizing hyperparameters of various machine learning algorithms. Those methods adopt probabilistic surrogate models like Gaussian processes to approximate and minimize the validation error function of hyperparameter values. However, probabilistic surrogates require accurate estimates of sufficient statistics (e.g., covariance) of the error distribution and thus need many function evaluations with a …
Hyperparameter optimization (HPO) plays a central role in the automated machine learning (AutoML). It is a challenging task as the response surfaces of hyperparameters are generally unknown, hence essentially a global optimization problem. This paper reformulates HPO as a computer experiment and proposes a novel sequential uniform design (SeqUD) strategy with three-fold advantages: a) the hyperparameter space is adaptively explored with evenly spread design points, without the need of expensive meta-modeling and acquisition optimization; b) the batch-by-batch design points are sequentially gen…
University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Hyperparameter optimization and neural architecture search can become prohibitively expensive for regular black-box Bayesian optimization because the training and evaluation of a single model can easily take several hours. To overcome this, we introduce a comprehensive tool suite for effective multi-fidelity Bayesian optimization and the analysis of its runs. The suite, written in Python, provides a simple way to specify complex design spaces, a robust and efficient combination of Bayesian optimization and HyperBand, and a comprehensive analysis of the optimization process and its outcomes.
University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Bayesian Optimization (BO) is a common approach for hyperparameter optimization (HPO) in automated machine learning. Although it is well-accepted that HPO is crucial to obtain well-performing machine learning models, tuning BO's own hyperparameters is often neglected. In this paper, we empirically study the impact of optimizing BO's own hyperparameters and the transferability of the found settings using a wide range of benchmarks, including artificial functions, HPO and HPO combined with neural architecture search. In particular, we show (i) that tuning can improve the any-time performance of …
Université Laval（拉瓦尔大学）；École de technologie supérieure（高等技术学院）
In this paper, we bridge the gap between hyperparameter optimization and ensemble learning by performing Bayesian optimization of an ensemble with regards to its hyperparameters. Our method consists in building a fixed-size ensemble, optimizing the configuration of one classifier of the ensemble at each iteration of the hyperparameter optimization algorithm, taking into consideration the interaction with the other models when evaluating potential performances. We also consider the case where the ensemble is to be reconstructed at the end of the hyperparameter optimization phase, through a gree…
The hyperparameter optimization of neural network can be expressed as a bilevel optimization problem. The bilevel optimization is used to automatically update the hyperparameter, and the gradient of the hyperparameter is the approximate gradient based on the best response function. Finding the best response function is very time consuming. In this paper we propose CPMLHO, a new hyperparameter optimization method using cutting plane method and mixed-level objective function.The cutting plane is added to the inner layer to constrain the space of the response function. To obtain more accurate hyp…
Gradient-based hyperparameter optimization has earned a widespread popularity in the context of few-shot meta-learning, but remains broadly impractical for tasks with long horizons (many gradient steps), due to memory scaling and gradient degradation issues. A common workaround is to learn hyperparameters online, but this introduces greediness which comes with a significant performance drop. We propose forward-mode differentiation with sharing (FDS), a simple and efficient algorithm which tackles memory scaling issues with forward-mode differentiation, and gradient degradation issues by sharin…
University of Milano-Bicocca（米兰比可卡大学）；OAKS srl（OAKS有限责任公司）
There is a consensus that focusing only on accuracy in searching for optimal machine learning models amplifies biases contained in the data, leading to unfair predictions and decision supports. Recently, multi-objective hyperparameter optimization has been proposed to search for machine learning models which offer equally Pareto-efficient trade-offs between accuracy and fairness. Although these approaches proved to be more versatile than fairness-aware machine learning algorithms -- which optimize accuracy constrained to some threshold on fairness -- they could drastically increase the energy …
CEREMADE（CEREMADE（巴黎多芬大学数学与决策研究中心））；CNRS（法国国家科学研究中心）；Université Paris-Dauphine（巴黎多芬大学）；PSL Research University（巴黎文理研究大学）；École Normale Supérieure（巴黎高等师范学院）
Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and …
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Department of Mathematics, Cornell University（数学系，康奈尔大学）；Department of Computing and Mathematical Sciences, California Institute of Technology（计算与数学科学系，加州理工学院）
Twitter（推特）；Facebook（脸书）；SigOpt, an Intel company（SigOpt（英特尔公司旗下））；Valohai；Paradigm（第四范式）；ChaLearn
This paper presents the results and insights from the black-box optimization (BBO) challenge at NeurIPS 2020 which ran from July-October, 2020. The challenge emphasized the importance of evaluating derivative-free optimizers for tuning the hyperparameters of machine learning models. This was the first black-box optimization challenge with a machine learning emphasis. It was based on tuning (validation set) performance of standard machine learning models on real datasets. This competition has widespread impact as black-box optimization (e.g., Bayesian optimization) is relevant for hyperparamete…
