Multi-objective optimization is a crucial matter in computer systems design space exploration because real-world applications often rely on a trade-off between several objectives. Derivatives are usually not available or impractical to compute and the feasibility of an experiment can not always be determined in advance. These problems are particularly difficult when the feasible region is relatively small, and it may be prohibitive to even find a feasible experiment, let alone an optimal one. We introduce a new methodology and corresponding software framework, HyperMapper 2.0, which handles multi-objective optimization, unknown feasibility constraints, and categorical ordinal variables. This new methodology also supports injection of user prior knowledge in the search when available. All of these features are common requirements in computer systems but rarely exposed in existing design space exploration systems. The proposed methodology follows a white-box model which is simple to understand and interpret (unlike, for example, neural networks) and can be used by the user to better understand the results of the automatic search. We apply and evaluate the new methodology to automatic static tuning of hardware accelerators within the recently introduced Spatial programming language, with minimization of design runtime and compute logic under the constraint of the design fitting in a target field programmable gate array chip. Our results show that HyperMapper 2.0 provides better Pareto fronts compared to state-of-the-art baselines, with better or competitive hypervolume indicator and with 8x improvement in sampling budget for most of the benchmarks explored.
Our work is similar in nature to the approaches adopted in the Bayesian optimization literature @cite_6 . Example of widely used mono-objective Bayesian DFO software are SMAC @cite_32 , SpearMint @cite_14 @cite_12 and the work on tree-structured Parzen estimator (TPE) @cite_1 . These mono-objective methodologies are based on random forests, Gaussian processes and TPEs making the choice of learned models varied.
@cite_14 @cite_1 @cite_32 @cite_6 @cite_12
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Bayesian optimization has recently emerged as a powerful and flexible tool in machine learning for hyperparameter tuning and more generally for the ecient global optimization of expensive black box functions. The established practice requires a user-defined bounded domain, which is assumed to contain the global optimizer. However, when little is known about the probed objective function, it can be dicult to prescribe such a domain. In this work, we modify the standard Bayesian optimization framework in a principled way to allow for unconstrained exploration of the search space. We introduce a new alternative method and compare it to a volume doubling baseline on two common synthetic benchmarking test functions. Finally, we apply our proposed methods on the task of tuning the stochastic gradient descent optimizer for both a multi-layered perceptron and a convolutional neural network on the MNIST dataset. Three Bayesian related approaches, namely, variational Bayesian (VB), minimum message length (MML) and Bayesian Ying-Yang (BYY) harmony learning, have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model (GMM). This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart (DNW) prior on GMM. In addition to adopting the existing algorithms either directly or with some modifications, the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap. The performances of automatic model selection are evaluated through extensive experiments, with several empirical findings: 1) Considering priors merely on the mixing weights, each of three approaches makes biased mistakes, while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance. 2) As Jeffreys prior is replaced by the DNW prior, all the three approaches improve their performances. Moreover, Jeffreys prior makes MML slightly better than VB, while the DNW prior makes VB better than MML. 3) As the hyperparameters of DNW prior are further optimized by each of its own learning principle, BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters. Actually, VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior. 4) BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized. Being different from VB and MML that rely on appropriate priors to perform model selection, BYY does not highly depend on the type of priors. It has model selection ability even without priors and performs already very well with Jeffreys prior, and incrementally improves as Jeffreys prior is replaced by the DNW prior. Finally, all algorithms are applied on the Berkeley segmentation database of real world images. Again, BYY considerably outperforms both VB and MML, especially in detecting the objects of interest from a confusing background. A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained. Bayesian optimization has recently been proposed as a framework for automatically tuning the hyperparameters of machine learning models and has been shown to yield state-of-the-art performance with impressive ease and efficiency. In this paper, we explore whether it is possible to transfer the knowledge gained from previous optimizations to new tasks in order to find optimal hyperparameter settings more efficiently. Our approach is based on extending multi-task Gaussian processes to the framework of Bayesian optimization. We show that this method significantly speeds up the optimization process when compared to the standard single-task approach. We further propose a straightforward extension of our algorithm in order to jointly minimize the average error across multiple tasks and demonstrate how this can be used to greatly speed up k-fold cross-validation. Lastly, we propose an adaptation of a recently developed acquisition function, entropy search, to the cost-sensitive, multi-task setting. We demonstrate the utility of this new acquisition function by leveraging a small dataset to explore hyper-parameter settings for a large dataset. Our algorithm dynamically chooses which dataset to query in order to yield the most information per unit cost.