Finding optimal parameter configurations for tunable GPU kernels is a non-trivial exercise for large search spaces, even when automated. This poses an optimization task on a non-convex search space, using an expensive to evaluate function with unknown derivative. These characteristics make a good candidate for Bayesian Optimization, which has not been applied to this problem before. However, the application of Bayesian Optimization to this problem is challenging. We demonstrate how to deal with the rough, discrete, constrained search spaces, containing invalid configurations. We introduce a novel contextual variance exploration factor, as well as new acquisition functions with improved scalability, combined with an informed acquisition function selection mechanism. By comparing the performance of our Bayesian Optimization implementation on various test cases to the existing search strategies in Kernel Tuner, as well as other Bayesian Optimization implementations, we demonstrate that our search strategies generalize well and consistently outperform other search strategies by a wide margin.
Physical simulation-based optimization is a common task in science and engineering. Many such simulations produce image- or tensor-based outputs where the desired objective is a function of those outputs, and optimization is performed over a high-dimensional parameter space. We develop a Bayesian optimization method leveraging tensor-based Gaussian process surrogates and trust region Bayesian optimization to effectively model the image outputs and to efficiently optimize these types of simulations, including a radio-frequency tower configuration problem and an optical design problem.
In this work, we introduce a novel workflow that couples robotics to machine-learning for efficient optimization of a non-aqueous battery electrolyte. A custom-built automated experiment named "Clio" is coupled to Dragonfly - a Bayesian optimization-based experiment planner. Clio autonomously optimizes electrolyte conductivity over a single-salt, ternary solvent design space. Using this workflow, we identify 6 fast-charging electrolytes in 2 work-days and 42 experiments (compared with 60 days using exhaustive search of the 1000 possible candidates, or 6 days assuming only 10% of candidates are evaluated). Our method finds the highest reported conductivity electrolyte in a design space heavily explored by previous literature, converging on a high-conductivity mixture that demonstrates subtle electrolyte chemical physics.
Automated hyperparameter optimization (HPO) has gained great popularity and is an important ingredient of most automated machine learning frameworks. The process of designing HPO algorithms, however, is still an unsystematic and manual process: Limitations of prior work are identified and the improvements proposed are -- even though guided by expert knowledge -- still somewhat arbitrary. This rarely allows for gaining a holistic understanding of which algorithmic components are driving performance, and carries the risk of overlooking good algorithmic design choices. We present a principled approach to automated benchmark-driven algorithm design applied to multifidelity HPO (MF-HPO): First, we formalize a rich space of MF-HPO candidates that includes, but is not limited to common HPO algorithms, and then present a configurable framework covering this space. To find the best candidate automatically and systematically, we follow a programming-by-optimization approach and search over the space of algorithm candidates via Bayesian optimization. We challenge whether the found design choices are necessary or could be replaced by more naive and simpler ones by performing an ablation analysis. We observe that using a relatively simple configuration, in some ways simpler than established methods, performs very well as long as some critical configuration parameters have the right value.
An essential task of Automated Machine Learning (AutoML) is the problem of automatically finding the pipeline with the best generalization performance on a given dataset. This problem has been addressed with sophisticated black-box optimization techniques such as Bayesian Optimization, Grammar-Based Genetic Algorithms, and tree search algorithms. Most of the current approaches are motivated by the assumption that optimizing the components of a pipeline in isolation may yield sub-optimal results. We present Naive AutoML, an approach that does precisely this: It optimizes the different algorithms of a pre-defined pipeline scheme in isolation. The finally returned pipeline is obtained by just taking the best algorithm of each slot. The isolated optimization leads to substantially reduced search spaces, and, surprisingly, this approach yields comparable and sometimes even better performance than current state-of-the-art optimizers.
The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO method and explore how the low-rank factorization of the convolutional weights of intermediate layers of a convolutional neural network can be used to define an analytical response surface for optimizing hyper-parameters, using only training data. We quantify how this surface behaves as a surrogate to model performance and can be solved using a trust-region search algorithm, which we call autoHyper. The algorithm outperforms state-of-the-art such as Bayesian Optimization and generalizes across model, optimizer, and dataset selection. Our code can be found at \url{https://github.com/MathieuTuli/autoHyper}.
This paper presents the data-driven techniques and methodologies used to predict the remaining useful life (RUL) of a fleet of aircraft engines that can suffer failures of diverse nature. The solution presented is based on two Deep Convolutional Neural Networks (DCNN) stacked in two levels. The first DCNN is used to extract a low-dimensional feature vector using the normalized raw data as input. The second DCNN ingests a list of vectors taken from the former DCNN and estimates the RUL. Model selection was carried out by means of Bayesian optimization using a repeated random subsampling validation approach. The proposed methodology was ranked in the third place of the 2021 PHM Conference Data Challenge.
This article is a companion paper to our earlier work Miroshnikov et al. (2021) on fairness interpretability, which introduces bias explanations. In the current work, we propose a bias mitigation methodology based upon the construction of post-processed models with fairer regressor distributions for Wasserstein-based fairness metrics. By identifying the list of predictors contributing the most to the bias, we reduce the dimensionality of the problem by mitigating the bias originating from those predictors. The post-processing methodology involves reshaping the predictor distributions by balancing the positive and negative bias explanations and allows for the regressor bias to decrease. We design an algorithm that uses Bayesian optimization to construct the bias-performance efficient frontier over the family of post-processed models, from which an optimal model is selected. Our novel methodology performs optimization in low-dimensional spaces and avoids expensive model retraining.
Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for offline studies and thus, cannot be applied for online transient stability prediction, which is a major requirement in modern power systems. This motivated the requirement to apply an artificial intelligence-based approach. In this regard, supervised machine learning is beneficial for predicting transient stability status, in the presence of uncertainties. Therefore, this paper examines the application of a binary support vector machine-based supervised machine learning, for predicting the transient stability status of a power system, considering uncertainties of various factors, such as load, faulted line, fault type, fault location and fault clearing time. The support vector machine is trained using a Gaussian Radial Basis function kernel and its hyperparameters are optimized using Bayesian optimization. Results obtained for the IEEE 14-bus test system demonstrated that the proposed method offers a fast technique for probabilistic transient stability status prediction, with an excellent accuracy. DIgSILENT PowerFactory and MATLAB was utilized for transient stability time-domain simulations (for obtaining training data for support vector machine) and for applying support vector machine, respectively.
Optimization problems are crucial in artificial intelligence. Optimization algorithms are generally used to adjust the performance of artificial intelligence models to minimize the error of mapping inputs to outputs. Current evaluation methods on optimization algorithms generally consider the performance in terms of quality. However, not all optimization algorithms for all test cases are evaluated equal from quality, the computation time should be also considered for optimization tasks. In this paper, we investigate the quality and computation time of optimization algorithms in optimization problems, instead of the one-for-all evaluation of quality. We select the well-known optimization algorithms (Bayesian optimization and evolutionary algorithms) and evaluate them on the benchmark test functions in terms of quality and computation time. The results show that BO is suitable to be applied in the optimization tasks that are needed to obtain desired quality in the limited function evaluations, and the EAs are suitable to search the optimal of the tasks that are allowed to find the optimal solution with enough function evaluations. This paper provides the recommendation to select suitable optimization algorithms for optimization problems with different numbers of function evaluations, which contributes to the efficiency that obtains the desired quality with less computation time for optimization problems.
Bayesian optimization is a powerful paradigm to optimize black-box functions based on scarce and noisy data. Its data efficiency can be further improved by transfer learning from related tasks. While recent transfer models meta-learn a prior based on large amount of data, in the low-data regime methods that exploit the closed-form posterior of Gaussian processes (GPs) have an advantage. In this setting, several analytically tractable transfer-model posteriors have been proposed, but the relative advantages of these methods are not well understood. In this paper, we provide a unified view on hierarchical GP models for transfer learning, which allows us to analyze the relationship between methods. As part of the analysis, we develop a novel closed-form boosted GP transfer model that fits between existing approaches in terms of complexity. We evaluate the performance of the different approaches in large-scale experiments and highlight strengths and weaknesses of the different transfer-learning methods.
Recent advances in computationally efficient non-myopic Bayesian optimization offer improved query efficiency over traditional myopic methods like expected improvement, with only a modest increase in computational cost. These advances have been largely limited to unconstrained BO methods with only a few exceptions which require heavy computation. For instance, one existing multi-step lookahead constrained BO method (Lam & Willcox, 2017) relies on computationally expensive unreliable brute force derivative-free optimization of a Monte Carlo rollout acquisition function. Methods that use the reparameterization trick for more efficient derivative-based optimization of non-myopic acquisition functions in the unconstrained setting, like sample average approximation and infinitesimal perturbation analysis, do not extend: constraints introduce discontinuities in the sampled acquisition function surface. Moreover, we argue here that being non-myopic is even more important in constrained problems because fear of violating constraints pushes myopic methods away from sampling the boundary between feasible and infeasible regions, slowing the discovery of optimal solutions with tight constraints. In this paper, we propose a computationally efficient two-step lookahead constrained Bayesian optimization acquisition function (2-OPT-C) supporting both sequential and batch settings. To enable fast acquisition function optimization, we develop a novel likelihood ratio-based unbiased estimator of the gradient of the two-step optimal acquisition function that does not use the reparameterization trick. In numerical experiments, 2-OPT-C typically improves query efficiency by 2x or more over previous methods, and in some cases by 10x or more.
Complex processes in science and engineering are often formulated as multistage decision-making problems. In this paper, we consider a type of multistage decision-making process called a cascade process. A cascade process is a multistage process in which the output of one stage is used as an input for the subsequent stage. When the cost of each stage is expensive, it is difficult to search for the optimal controllable parameters for each stage exhaustively. To address this problem, we formulate the optimization of the cascade process as an extension of the Bayesian optimization framework and propose two types of acquisition functions based on credible intervals and expected improvement. We investigate the theoretical properties of the proposed acquisition functions and demonstrate their effectiveness through numerical experiments. In addition, we consider an extension called suspension setting in which we are allowed to suspend the cascade process at the middle of the multistage decision-making process that often arises in practical problems. We apply the proposed method in a test problem involving a solar cell simulator, which was the motivation for this study.
Bayesian optimization (BO) with Gaussian processes (GP) as surrogate models is widely used to optimize analytically unknown and expensive-to-evaluate functions. In this paper, we propose Prior-mean-RObust Bayesian Optimization (PROBO) that outperforms classical BO on specific problems. First, we study the effect of the Gaussian processes' prior specifications on classical BO's convergence. We find the prior's mean parameters to have the highest influence on convergence among all prior components. In response to this result, we introduce PROBO as a generalization of BO that aims at rendering the method more robust towards prior mean parameter misspecification. This is achieved by explicitly accounting for GP imprecision via a prior near-ignorance model. At the heart of this is a novel acquisition function, the generalized lower confidence bound (GLCB). We test our approach against classical BO on a real-world problem from material science and observe PROBO to converge faster. Further experiments on multimodal and wiggly target functions confirm the superiority of our method.
Optimizing parameterized quantum circuits is a key routine in using near-term quantum devices. However, the existing algorithms for such optimization require an excessive number of quantum-measurement shots for estimating expectation values of observables and repeating many iterations, whose cost has been a critical obstacle for practical use. We develop an efficient alternative optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO), to address this problem. SGLBO reduces the measurement-shot cost by estimating an appropriate direction of updating circuit parameters based on stochastic gradient descent (SGD) and further utilizing Bayesian optimization (BO) to estimate the optimal step size for each iteration in SGD. In addition, we formulate an adaptive measurement-shot strategy and introduce a technique of suffix averaging to reduce the effect of statistical and hardware noise. Our numerical simulation demonstrates that the SGLBO augmented with these techniques can drastically reduce the measurement-shot cost, improve the accuracy, and make the optimization noise-robust.
Bayesian optimization (BO) is a sample-efficient approach to optimizing costly-to-evaluate black-box functions. Most BO methods ignore how evaluation costs may vary over the optimization domain. However, these costs can be highly heterogeneous and are often unknown in advance. This occurs in many practical settings, such as hyperparameter tuning of machine learning algorithms or physics-based simulation optimization. Moreover, those few existing methods that acknowledge cost heterogeneity do not naturally accommodate a budget constraint on the total evaluation cost. This combination of unknown costs and a budget constraint introduces a new dimension to the exploration-exploitation trade-off, where learning about the cost incurs the cost itself. Existing methods do not reason about the various trade-offs of this problem in a principled way, leading often to poor performance. We formalize this claim by proving that the expected improvement and the expected improvement per unit of cost, arguably the two most widely used acquisition functions in practice, can be arbitrarily inferior with respect to the optimal non-myopic policy. To overcome the shortcomings of existing approaches, we propose the budgeted multi-step expected improvement, a non-myopic acquisition function that generalizes classical expected improvement to the setting of heterogeneous and unknown evaluation costs. Finally, we show that our acquisition function outperforms existing methods in a variety of synthetic and real problems.
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes within a Bayesian optimization framework. The proposed scheme uses two Gaussian processes for the stochastic system, one emulates the (known) process model, and another, the true system through measurements. In this way, low fidelity samples can be obtained via a model, while high fidelity samples are obtained through measurements of the system. This framework captures the system's behavior in a non-parametric fashion while driving exploration through acquisition functions. The benefit of using a Gaussian process to represent the system is the ability to perform uncertainty quantification in real-time and allow for chance constraints to be satisfied with high confidence. This results in a practical approach that is illustrated in numerical case studies, including a semi-batch photobioreactor optimization problem.
Because of its sample efficiency, Bayesian optimization (BO) has become a popular approach dealing with expensive black-box optimization problems, such as hyperparameter optimization (HPO). Recent empirical experiments showed that the loss landscapes of HPO problems tend to be more benign than previously assumed, i.e. in the best case uni-modal and convex, such that a BO framework could be more efficient if it can focus on those promising local regions. In this paper, we propose BOinG, a two-stage approach that is tailored toward mid-sized configuration spaces, as one encounters in many HPO problems. In the first stage, we build a scalable global surrogate model with a random forest to describe the overall landscape structure. Further, we choose a promising subregion via a bottom-up approach on the upper-level tree structure. In the second stage, a local model in this subregion is utilized to suggest the point to be evaluated next. Empirical experiments show that BOinG is able to exploit the structure of typical HPO problems and performs particularly well on mid-sized problems from synthetic functions and HPO.
Bayesian Optimization is an effective method for searching the global maxima of an objective function especially if the function is unknown. The process comprises of using a surrogate function and choosing an acquisition function followed by optimizing the acquisition function to find the next sampling point. This paper analyzes different acquistion functions like Maximum Probability of Improvement and Expected Improvement and various optimizers like L-BFGS and TNC to optimize the acquisitions functions for finding the next sampling point. Along with the analysis of time taken, the paper also shows the importance of position of initial samples chosen.
Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final model performance. This lack of explainability makes it difficult to trust and understand the automated HPO process and its results. We suggest using interpretable machine learning (IML) to gain insights from the experimental data obtained during HPO with Bayesian optimization (BO). BO tends to focus on promising regions with potential high-performance configurations and thus induces a sampling bias. Hence, many IML techniques, such as the partial dependence plot (PDP), carry the risk of generating biased interpretations. By leveraging the posterior uncertainty of the BO surrogate model, we introduce a variant of the PDP with estimated confidence bands. We propose to partition the hyperparameter space to obtain more confident and reliable PDPs in relevant sub-regions. In an experimental study, we provide quantitative evidence for the increased quality of the PDPs within sub-regions.