Designing functional molecules and advanced materials requires complex design choices: tuning continuous process parameters such as temperatures or flow rates, while simultaneously selecting catalysts or solvents. To date, the development of data-driven experiment planning strategies for autonomous experimentation has largely focused on continuous process parameters despite the urge to devise efficient strategies for the selection of categorical variables. Here, we introduce Gryffin, a general purpose optimization framework for the autonomous selection of categorical variables driven by expert knowledge. Gryffin augments Bayesian optimization based on kernel density estimation with smooth approximations to categorical distributions. Leveraging domain knowledge in the form of physicochemical descriptors, Gryffin can significantly accelerate the search for promising molecules and materials. Gryffin can further highlight relevant correlations between the provided descriptors to inspire physical insights and foster scientific intuition. In addition to comprehensive benchmarks, we demonstrate the capabilities and performance of Gryffin on three examples in materials science and chemistry: (i) the discovery of non-fullerene acceptors for organic solar cells, (ii) the design of hybrid organic-inorganic perovskites for light harvesting, and (iii) the identification of ligands and process parameters for Suzuki-Miyaura reactions. Our results suggest that Gryffin, in its simplest form, is competitive with state-of-the-art categorical optimization algorithms. However, when leveraging domain knowledge provided via descriptors, Gryffin outperforms other approaches while simultaneously refining this domain knowledge to promote scientific understanding.
Most research in Bayesian optimization (BO) has focused on \emph{direct feedback} scenarios, where one has access to exact values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine learning hyper-parameter configuration problems. However, in domains such as modelling human preferences, A/B tests, or recommender systems, there is a need for methods that can replace direct feedback with \emph{preferential feedback}, obtained via rankings or pairwise comparisons. In this work, we present preferential batch Bayesian optimization (PBBO), a new framework that allows finding the optimum of a latent function of interest, given any type of parallel preferential feedback for a group of two or more points. We do so by using a Gaussian process model with a likelihood specially designed to enable parallel and efficient data collection mechanisms, which are key in modern machine learning. We show how the acquisitions developed under this framework generalize and augment previous approaches in Bayesian optimization, expanding the use of these techniques to a wider range of domains. An extensive simulation study shows the benefits of this approach, both with simulated functions and four real data sets.
Bayesian optimization (BO) is a class of global optimization algorithms, suitable for minimizing an expensive objective function in as few function evaluations as possible. While BO budgets are typically given in iterations, this implicitly measures convergence in terms of iteration count and assumes each evaluation has identical cost. In practice, evaluation costs may vary in different regions of the search space. For example, the cost of neural network training increases quadratically with layer size, which is a typical hyperparameter. Cost-aware BO measures convergence with alternative cost metrics such as time, energy, or money, for which vanilla BO methods are unsuited. We introduce Cost Apportioned BO (CArBO), which attempts to minimize an objective function in as little cost as possible. CArBO combines a cost-effective initial design with a cost-cooled optimization phase which depreciates a learned cost model as iterations proceed. On a set of 20 black-box function optimization problems we show that, given the same cost budget, CArBO finds significantly better hyperparameter configurations than competing methods.
Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a multi-armed bandit problem, where the payoff function is sampled from a Gaussian process (GP). Further, we focus on action selections via upper confidence bound (UCB) or expected improvement (EI) due to their prevalent use in practice. Prior works using GPs for bandits cannot allow the iteration horizon $T$ to be large, as the complexity of computing the posterior parameters scales cubically with the number of past observations. To circumvent this computational burden, we propose a simple statistical test: only incorporate an action into the GP posterior when its conditional entropy exceeds an $\epsilon$ threshold. Doing so permits us to precisely characterize the trade-off between regret bounds of GP bandit algorithms and complexity of the posterior distributions depending on the compression parameter $\epsilon$ for both discrete and continuous action sets. To best of our knowledge, this is the first result which allows us to obtain sublinear regret bounds while still maintaining sublinear growth rate of the complexity of the posterior which is linear in the existing literature. Moreover, a provably finite bound on the complexity could be achieved but the algorithm would result in $\epsilon$-regret which means $\textbf{Reg}_T/T \rightarrow \mathcal{O}(\epsilon)$ as $T\rightarrow \infty$. Experimentally, we observe state of the art accuracy and complexity trade-offs for GP bandit algorithms applied to global optimization, suggesting the merits of compressed GPs in bandit settings.
We introduce a model-based asynchronous multi-fidelity method for hyperparameter and neural architecture search that combines the strengths of asynchronous Hyperband and Gaussian process-based Bayesian optimization. At the heart of our method is a probabilistic model that can simultaneously reason across hyperparameters and resource levels, and supports decision-making in the presence of pending evaluations. We demonstrate the effectiveness of our method on a wide range of challenging benchmarks, for tabular data, image classification and language modelling, and report substantial speed-ups over current state-of-the-art methods. Our new methods, along with asynchronous baselines, are implemented in a distributed framework which will be open sourced along with this publication.
High-fidelity complex engineering simulations are highly predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. In this paper, an asynchronous constrained batch-parallel Bayesian optimization method is proposed to efficiently solve the computationally-expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantages of this method are three-fold. First, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated massively parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the method can handle both known and unknown constraints. Third, the proposed method considers several acquisition functions at the same time and sample based on an evolving probability mass distribution function using a modified GP-Hedge scheme, where parameters are corresponding to the performance of each acquisition function. The proposed framework is termed aphBO-2GP-3B, which corresponds to asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The aphBO-2GP-3B framework is demonstrated using two high-fidelity expensive industrial applications, where the first one is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.
Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is noisy. The most popular application of bayesian optimization is the automatic hyperparameter tuning of machine learning algorithms, where we obtain the best configuration of machine learning algorithms by optimizing the estimation of the generalization error of these algorithms. Despite being applied with success, bayesian optimization methodologies also have hyperparameters that need to be configured such as the probabilistic surrogate model or the acquisition function used. A bad decision over the configuration of these hyperparameters implies obtaining bad quality results. Typically, these hyperparameters are tuned by making assumptions of the objective function that we want to evaluate but there are scenarios where we do not have any prior information about the objective function. In this paper, we propose a first attempt over automatic bayesian optimization by exploring several heuristics that automatically tune the acquisition function of bayesian optimization. We illustrate the effectiveness of these heurisitcs in a set of benchmark problems and a hyperparameter tuning problem of a machine learning algorithm.
With the rise of the digital economy and an explosion of available information about consumers, effective personalization of goods and services has become a core business focus for companies to improve revenues and maintain a competitive edge. This paper studies the personalization problem through the lens of policy learning, where the goal is to learn a decision-making rule (a policy) that maps from consumer and product characteristics (features) to recommendations (actions) in order to optimize outcomes (rewards). We focus on using available historical data for offline learning with unknown data collection procedures, where a key challenge is the non-random assignment of recommendations. Moreover, in many business and medical applications, interpretability of a policy is essential. We study the class of policies with linear decision boundaries to ensure interpretability, and propose learning algorithms using tools from causal inference to address unbalanced treatments. We study several optimization schemes to solve the associated non-convex, non-smooth optimization problem, and find that a Bayesian optimization algorithm is effective. We test our algorithm with extensive simulation studies and apply it to an anonymized online marketplace customer purchase dataset, where the learned policy outputs a personalized discount recommendation based on customer and product features in order to maximize gross merchandise value (GMV) for sellers. Our learned policy improves upon the platform's baseline by 88.2\% in net sales revenue, while also providing informative insights on which features are important for the decision-making process. Our findings suggest that our proposed policy learning framework using tools from causal inference and Bayesian optimization provides a promising practical approach to interpretable personalization across a wide range of applications.
The Gaussian process bandit is a problem in which we want to find a maximizer of a black-box function with the minimum number of function evaluations. If the black-box function varies with time, then time-varying Bayesian optimization is a promising framework. However, a drawback with current methods is in the assumption that the evaluation time for every observation is constant, which can be unrealistic for many practical applications, e.g., recommender systems and environmental monitoring. As a result, the performance of current methods can be degraded when this assumption is violated. To cope with this problem, we propose a novel time-varying Bayesian optimization algorithm that can effectively handle the non-constant evaluation time. Furthermore, we theoretically establish a regret bound of our algorithm. Our bound elucidates that a pattern of the evaluation time sequence can hugely affect the difficulty of the problem. We also provide experimental results to validate the practical effectiveness of the proposed method.
Modelling human function learning has been the subject of in-tense research in cognitive sciences. The topic is relevant in black-box optimization where information about the objective and/or constraints is not available and must be learned through function evaluations. In this paper we focus on the relation between the behaviour of humans searching for the maximum and the probabilistic model used in Bayesian Optimization. As surrogate models of the unknown function both Gaussian Processes and Random Forest have been considered: the Bayesian learning paradigm is central in the development of active learning approaches balancing exploration/exploitation in uncertain conditions towards effective generalization in large decision spaces. In this paper we analyse experimentally how Bayesian Optimization compares to humans searching for the maximum of an unknown 2D function. A set of controlled experiments with 60 subjects, using both surrogate models, confirm that Bayesian Optimization provides a general model to represent individual patterns of active learning in humans
Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian Process, and builds, depending on its mean and variance, an acquisition function whose optimizer yields the new evaluation point, leading to update the probabilistic surrogate model. Despite its sample efficiency, Bayesian Optimiza-tion does not scale well with the dimensions of the problem. The optimization of the acquisition function has received less attention because its computational cost is usually considered negligible compared to that of the evaluation of the objec-tive function. Its efficient optimization is often inhibited, particularly in high di-mensional problems, by multiple extrema. In this paper we leverage the addition-ality of the objective function into mapping both the kernel and the acquisition function of the Bayesian Optimization in lower dimensional subspaces. This ap-proach makes more efficient the learning/updating of the probabilistic surrogate model and allows an efficient optimization of the acquisition function. Experi-mental results are presented for real-life application, that is the control of pumps in urban water distribution systems.
Deep learning for computer vision depends on lossy image compression: it reduces the storage required for training and test data and lowers transfer costs in deployment. Mainstream datasets and imaging pipelines all rely on standard JPEG compression. In JPEG, the degree of quantization of frequency coefficients controls the lossiness: an 8 by 8 quantization table (Q-table) decides both the quality of the encoded image and the compression ratio. While a long history of work has sought better Q-tables, existing work either seeks to minimize image distortion or to optimize for models of the human visual system. This work asks whether JPEG Q-tables exist that are "better" for specific vision networks and can offer better quality--size trade-offs than ones designed for human perception or minimal distortion. We reconstruct an ImageNet test set with higher resolution to explore the effect of JPEG compression under novel Q-tables. We attempt several approaches to tune a Q-table for a vision task. We find that a simple sorted random sampling method can exceed the performance of the standard JPEG Q-table. We also use hyper-parameter tuning techniques including bounded random search, Bayesian optimization, and composite heuristic optimization methods. The new Q-tables we obtained can improve the compression rate by 10% to 200% when the accuracy is fixed, or improve accuracy up to $2\%$ at the same compression rate.
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian Optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists in a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches.
Sparse, knot-based Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Certain sparse models can be derived through specific variational approximations to the true posterior, and knots can be selected to minimize the Kullback-Leibler divergence between the approximate and true posterior. While this has been a successful approach, simultaneous optimization of knots can be slow due to the number of parameters being optimized. Furthermore, there have been few proposed methods for selecting the number of knots, and no experimental results exist in the literature. We propose using a one-at-a-time knot selection algorithm based on Bayesian optimization to select the number and locations of knots. We showcase the competitive performance of this method relative to simultaneous optimization of knots on three benchmark data sets, but at a fraction of the computational cost.
When learning policies for robot control, the required real-world data is typically prohibitively expensive to acquire, so learning in simulation is a popular strategy. Unfortunately, such polices are often not transferable to the real world due to a mismatch between the simulation and reality, called 'reality gap'. Domain randomization methods tackle this problem by randomizing the physics simulator (source domain) during training according to a distribution over domain parameters in order to obtain more robust policies that are able to overcome the reality gap. Most domain randomization approaches sample the domain parameters from a fixed distribution. This solution is suboptimal in the context of sim-to-real transferability, since it yields policies that have been trained without explicitly optimizing for the reward on the real system (target domain). Additionally, a fixed distribution assumes there is prior knowledge about the uncertainty over the domain parameters. In this paper, we propose Bayesian Domain Randomization (BayRn), a black-box sim-to-real algorithm that solves tasks efficiently by adapting the domain parameter distribution during learning given sparse data from the real-world target domain. BayRn uses Bayesian optimization to search the space of source domain distribution parameters such that this leads to a policy which maximizes the real-word objective, allowing for adaptive distributions during policy optimization. We experimentally validate the proposed approach in sim-to-sim as well as in sim-to-real experiments, comparing against three baseline methods on two robotic tasks. Our results show that BayRn is able to perform sim-to-real transfer, while significantly reducing the required prior knowledge.
This paper proposes the first-ever algorithmic framework for tuning hyper-parameters of stochastic optimization algorithm based on reinforcement learning. Hyper-parameters impose significant influences on the performance of stochastic optimization algorithms, such as evolutionary algorithms (EAs) and meta-heuristics. Yet, it is very time-consuming to determine optimal hyper-parameters due to the stochastic nature of these algorithms. We propose to model the tuning procedure as a Markov decision process, and resort the policy gradient algorithm to tune the hyper-parameters. Experiments on tuning stochastic algorithms with different kinds of hyper-parameters (continuous and discrete) for different optimization problems (continuous and discrete) show that the proposed hyper-parameter tuning algorithms do not require much less running times of the stochastic algorithms than bayesian optimization method. The proposed framework can be used as a standard tool for hyper-parameter tuning in stochastic algorithms.
Complex robot navigation and control problems can be framed as policy search problems. However, interactive learning in uncertain environments can be expensive, requiring the use of data-efficient methods. Bayesian optimization is an efficient nonlinear optimization method where queries are carefully selected to gather information about the optimum location. This is achieved by a surrogate model, which encodes past information, and the acquisition function for query selection. Bayesian optimization can be very sensitive to uncertainty in the input data or prior assumptions. In this work, we incorporate both robust optimization and statistical robustness, showing that both types of robustness are synergistic. For robust optimization we use an improved version of unscented Bayesian optimization which provides safe and repeatable policies in the presence of policy uncertainty. We also provide new theoretical insights. For statistical robustness, we use an adaptive surrogate model and we introduce the Boltzmann selection as a stochastic acquisition method to have convergence guarantees and improved performance even with surrogate modeling errors. We present results in several optimization benchmarks and robot tasks.
Scientific experiments are usually expensive due to complex experimental preparation and processing. Experimental design is therefore involved with the task of finding the optimal experimental input that results in the desirable output by using as few experiments as possible. Experimenters can often acquire the knowledge about the location of the global optimum. However, they do not know how to exploit this knowledge to accelerate experimental design. In this paper, we adopt the technique of Bayesian optimization for experimental design since Bayesian optimization has established itself as an efficient tool for optimizing expensive black-box functions. Again, it is unknown how to incorporate the expert prior knowledge about the global optimum into Bayesian optimization process. To address it, we represent the expert knowledge about the global optimum via placing a prior distribution on it and we then derive its posterior distribution. An efficient Bayesian optimization approach has been proposed via posterior sampling on the posterior distribution of the global optimum. We theoretically analyze the convergence of the proposed algorithm and discuss the robustness of incorporating expert prior. We evaluate the efficiency of our algorithm by optimizing synthetic functions and tuning hyperparameters of classifiers along with a real-world experiment on the synthesis of short polymer fiber. The results clearly demonstrate the advantages of our proposed method.
We introduce an open source python framework named PHS - Parallel Hyperparameter Search to enable hyperparameter optimization on numerous compute instances of any arbitrary python function. This is achieved with minimal modifications inside the target function. Possible applications appear in expensive to evaluate numerical computations which strongly depend on hyperparameters such as machine learning. Bayesian optimization is chosen as a sample efficient method to propose the next query set of parameters.
Bayesian optimization (BO) is a class of sample-efficient global optimization methods, where a probabilistic model conditioned on previous observations is used to determine future evaluations via the optimization of an acquisition function. Most acquisition functions are myopic, meaning that they only consider the impact of the next function evaluation. Non-myopic acquisition functions consider the impact of the next $h$ function evaluations and are typically computed through rollout, in which $h$ steps of BO are simulated. These rollout acquisition functions are defined as $h$-dimensional integrals, and are expensive to compute and optimize. We show that a combination of quasi-Monte Carlo, common random numbers, and control variates significantly reduce the computational burden of rollout. We then formulate a policy-search based approach that removes the need to optimize the rollout acquisition function. Finally, we discuss the qualitative behavior of rollout policies in the setting of multi-modal objectives and model error.