Downloads & Free Reading Options - Results

One of the key challenges facing the professionalservices delivery business is the issue of optimally balancingcompeting demands from multiple, concurrent engagementson a limited supply of skill resources. In this paper, wepresent a framework for combining causal Bayesian analysisand optimization to address this challenge. Our frameworkintegrates the identification and modeling of the impact ofvarious staffing factors on the delivery quality of individualengagements, and the optimization of the collective adjustmentsof these staffing factors, to maximize overall delivery qualityfor a pool of engagements. We describe a prototype systembuilt using this framework and actual services delivery datafrom IBM’s IT consulting business. System evaluation underrealistic scenarios constructed using historical delivery recordsprovides encouraging evidence that this framework can lead tosignificant delivery quality improvements. These initial resultsfurther open up exciting opportunities of additional future workin this area, including the integration of temporal relationshipsfor causal learning and multi-period optimization to addressmore complex business scenarios. ©2009 Microsoft Corporation. All rights reserved.

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 greedy selection over the pool of models generated during the optimization. We study the performance of our proposed method on three different hyperparameter spaces, showing that our approach is better than both the best single model and a greedy ensemble construction over the models produced by a standard Bayesian optimization.

Martin Pelikan, & David E. Goldberg (2000). Hierarchical Problem Solving by the Bayesian Optimization Algorithm. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-200), 267-274. Also IlliGAL Report No. 2000002. Abstract: The paper discusses three major issues. First, it discusses why it makes sense to approach problems in a hierarchical fashion. It defines the class of hierarchically decomposable functions that can be used to test the algorithms that approach problems in this fashion. Finally, the Bayesian optimization algorithm (BOA) is extended in order to solve the proposed class of problems.

Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method using the Expected Improvement policy and the results show substantial speedup with little impact on the performance in eight real and synthetic benchmarks.

Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples because the required doses are too high for imaging biological samples at high resolution. We propose the use of non-convex, Bayesian optimization to overcome this problem and reduce the dose required for successful reconstruction by two orders of magnitude compared to previous experiments. We suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution of 7.9 \AA$\,$ at a dose of 20 $e^- / \AA^2$. When averaging over only 15 low-dose datasets, a resolution of 4 \AA$\,$ is possible for large macromolecular complexes. With its independence from microscope transfer function, direct recovery of phase contrast and better scaling of signal-to-noise ratio, cryo-electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.

Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to contain the optimizer. However, when little is known about the probed objective function, it can be difficult to prescribe such bounds. In this work we modify the standard Bayesian optimization framework in a principled way to allow automatic resizing of the search space. We introduce two alternative methods and compare them on two common synthetic benchmarking test functions as well as the tasks of tuning the stochastic gradient descent optimizer of a multi-layered perceptron and a convolutional neural network on MNIST.

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tuning a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.

One of the goals of computer-aided surgery is to match intraoperative data to preoperative images of the anatomy and add complementary information that can facilitate the task of surgical navigation. In this context, mechanical palpation can reveal critical anatomical features such as arteries and cancerous lumps which are stiffer that the surrounding tissue. This work uses position and force measurements obtained during mechanical palpation for registration and stiffness mapping. Prior approaches, including our own, exhaustively palpated the entire organ to achieve this goal. To overcome the costly palpation of the entire organ, a Bayesian optimization framework is introduced to guide the end effector to palpate stiff regions while simultaneously updating the registration of the end effector to an a priori geometric model of the organ, hence enabling the fusion of ntraoperative data into the a priori model obtained through imaging. This new framework uses Gaussian processes to model the stiffness distribution and Bayesian optimization to direct where to sample next for maximum information gain. The proposed method was evaluated with experimental data obtained using a Cartesian robot interacting with a silicone organ model and an ex vivo porcine liver.

We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with decoupled constraints, in which subsets of the objective and constraint functions may be evaluated independently. For example, when the objective is evaluated on a CPU and the constraints are evaluated independently on a GPU. These problems require an acquisition function that can be separated into the contributions of the individual function evaluations. We develop one such acquisition function and call it Predictive Entropy Search with Constraints (PESC). PESC is an approximation to the expected information gain criterion and it compares favorably to alternative approaches based on improvement in several synthetic and real-world problems. In addition to this, we consider problems with a mix of functions that are fast and slow to evaluate. These problems require balancing the amount of time spent in the meta-computation of PESC and in the actual evaluation of the target objective. We take a bounded rationality approach and develop partial update for PESC which trades off accuracy against speed. We then propose a method for adaptively switching between the partial and full updates for PESC. This allows us to interpolate between versions of PESC that are efficient in terms of function evaluations and those that are efficient in terms of wall-clock time. Overall, we demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality.

We use Bayesian optimization to learn curricula for word representation learning, optimizing performance on downstream tasks that depend on the learned representations as features. The curricula are modeled by a linear ranking function which is the scalar product of a learned weight vector and an engineered feature vector that characterizes the different aspects of the complexity of each instance in the training corpus. We show that learning the curriculum improves performance on a variety of downstream tasks over random orders and in comparison to the natural corpus order.

We use Bayesian optimization to learn curricula for word representation learning, optimizing performance on downstream tasks that depend on the learned representations as features. The curricula are modeled by a linear ranking function which is the scalar product of a learned weight vector and an engineered feature vector that characterizes the different aspects of the complexity of each instance in the training corpus. We show that learning the curriculum improves performance on a variety of downstream tasks over random orders and in comparison to the natural corpus order.

We study the effect of taking correlation and budget constraints into consideration in practical Bayesian optimization tasks, such as active sensing and automated machine learning. We compare a large number of techniques from the bandits, experimental design and global optimization literature, including Thompson sampling, expected improvement (EI), probability of improvement (PI), Bayesian upper confidence bounds (BayesUCB and GPUCB). We also consider approaches specifically designed to take into account fixed budget constraints such as UBCE and gap-based methods. The latter methods perform worse than methods that take correlation into account in our fixed-budget settings. To remedy this, we introduce a novel adaptive Bayesian gap-based exploration method that simultaneously capitalizes on knowledge of the budget and correlation among the arms. The method outperforms the other techniques on a sensor network task, and on the domain of automatic machine learning technique selection and tuning.

Modern data science relies on data analytic pipelines to organize interdependent computational steps. Such analytic pipelines often involve different algorithms across multiple steps, each with its own hyperparameters. To achieve the best performance, it is often critical to select optimal algorithms and to set appropriate hyperparameters, which requires large computational efforts. Bayesian optimization provides a principled way for searching optimal hyperparameters for a single algorithm. However, many challenges remain in solving pipeline optimization problems with high-dimensional and highly conditional search space. In this work, we propose Fast LineAr SearcH (FLASH), an efficient method for tuning analytic pipelines. FLASH is a two-layer Bayesian optimization framework, which firstly uses a parametric model to select promising algorithms, then computes a nonparametric model to fine-tune hyperparameters of the promising algorithms. FLASH also includes an effective caching algorithm which can further accelerate the search process. Extensive experiments on a number of benchmark datasets have demonstrated that FLASH significantly outperforms previous state-of-the-art methods in both search speed and accuracy. Using 50% of the time budget, FLASH achieves up to 20% improvement on test error rate compared to the baselines. FLASH also yields state-of-the-art performance on a real-world application for healthcare predictive modeling.

We develop a framework for warm-starting Bayesian optimization, that reduces the solution time required to solve an optimization problem that is one in a sequence of related problems. This is useful when optimizing the output of a stochastic simulator that fails to provide derivative information, for which Bayesian optimization methods are well-suited. Solving sequences of related optimization problems arises when making several business decisions using one optimization model and input data collected over different time periods or markets. While many gradient-based methods can be warm started by initiating optimization at the solution to the previous problem, this warm start approach does not apply to Bayesian optimization methods, which carry a full metamodel of the objective function from iteration to iteration. Our approach builds a joint statistical model of the entire collection of related objective functions, and uses a value of information calculation to recommend points to evaluate.

We consider the problem of maximizing a real-valued continuous function $f$ using a Bayesian approach. Since the early work of Jonas Mockus and Antanas \v{Z}ilinskas in the 70's, the problem of optimization is usually formulated by considering the loss function $\max f - M_n$ (where $M_n$ denotes the best function value observed after $n$ evaluations of $f$). This loss function puts emphasis on the value of the maximum, at the expense of the location of the maximizer. In the special case of a one-step Bayes-optimal strategy, it leads to the classical Expected Improvement (EI) sampling criterion. This is a special case of a Stepwise Uncertainty Reduction (SUR) strategy, where the risk associated to a certain uncertainty measure (here, the expected loss) on the quantity of interest is minimized at each step of the algorithm. In this article, assuming that $f$ is defined over a measure space $(\mathbb{X}, \lambda)$, we propose to consider instead the integral loss function $\int_{\mathbb{X}} (f - M_n)_{+}\, d\lambda$, and we show that this leads, in the case of a Gaussian process prior, to a new numerically tractable sampling criterion that we call $\rm EI^2$ (for Expected Integrated Expected Improvement). A numerical experiment illustrates that a SUR strategy based on this new sampling criterion reduces the error on both the value and the location of the maximizer faster than the EI-based strategy.

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

In practice, the parameters of control policies are often tuned manually. This is time-consuming and frustrating. Reinforcement learning is a promising alternative that aims to automate this process, yet often requires too many experiments to be practical. In this paper, we propose a solution to this problem by exploiting prior knowledge from simulations, which are readily available for most robotic platforms. Specifically, we extend Entropy Search, a Bayesian optimization algorithm that maximizes information gain from each experiment, to the case of multiple information sources. The result is a principled way to automatically combine cheap, but inaccurate information from simulations with expensive and accurate physical experiments in a cost-effective manner. We apply the resulting method to a cart-pole system, which confirms that the algorithm can find good control policies with fewer experiments than standard Bayesian optimization on the physical system only.

When applying machine learning to problems in NLP, there are many choices to make about how to represent input texts. These choices can have a big effect on performance, but they are often uninteresting to researchers or practitioners who simply need a module that performs well. We propose an approach to optimizing over this space of choices, formulating the problem as global optimization. We apply a sequential model-based optimization technique and show that our method makes standard linear models competitive with more sophisticated, expensive state-of-the-art methods based on latent variable models or neural networks on various topic classification and sentiment analysis problems. Our approach is a first step towards black-box NLP systems that work with raw text and do not require manual tuning.

BayesOpt is a library with state-of-the-art Bayesian optimization methods to solve nonlinear optimization, stochastic bandits or sequential experimental design problems. Bayesian optimization is sample efficient by building a posterior distribution to capture the evidence and prior knowledge for the target function. Built in standard C++, the library is extremely efficient while being portable and flexible. It includes a common interface for C, C++, Python, Matlab and Octave.

We present PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. The central idea of PESMO is to choose evaluation points so as to maximally reduce the entropy of the posterior distribution over the Pareto set. Critically, the PESMO multi-objective acquisition function can be decomposed as a sum of objective-specific acquisition functions, which enables the algorithm to be used in \emph{decoupled} scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability also makes it possible to identify difficult objectives that require more evaluations. PESMO also offers gains in efficiency, as its cost scales linearly with the number of objectives, in comparison to the exponential cost of other methods. We compare PESMO with other related methods for multi-objective Bayesian optimization on synthetic and real-world problems. The results show that PESMO produces better recommendations with a smaller number of evaluations of the objectives, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.

Non-invasive brain stimulation, such as transcranial alternating current stimulation (tACS) provides a powerful tool to directly modulate brain oscillations that mediate complex cognitive processes. While the body of evidence about the effect of tACS on behavioral and cognitive performance is constantly growing, those studies fail to address the importance of subject- specific stimulation protocols. With this study here, we set the foundation to combine tACS with a recently presented framework that utilizes real-time fRMI and Bayesian optimization in order to identify the most optimal tACS protocol for a given individual. While Bayesian optimization is particularly relevant to such a scenario, its success depends on two fundamental choices: the choice of covariance kernel for the Gaussian process prior as well as the choice of acquisition function that guides the search. Using empirical (functional neuroimaging) as well as simulation data, we identified the squared exponential kernel and the upper confidence bound acquisition function to work best for our problem. These results will be used to inform our upcoming real- time experiments.

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.

We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately balance the load between the available machines to minimize the average SGD iteration time. Our experiments consider setups with over thirty parameters. Traditional Bayesian optimization, which uses a Gaussian process as its model, is not well suited to such high dimensional domains. To reduce convergence time, we exploit the available structure. We design a probabilistic model which simulates the behavior of distributed SGD and use it within Bayesian optimization. Our model can exploit many runtime measurements for inference per evaluation of the objective function. Our experiments show that our resulting optimizer converges to efficient configurations within ten iterations, the optimized configurations outperform those found by generic optimizer in thirty iterations by up to 2X.

An exciting branch of machine learning research focuses on methods for learning, optimizing, and integrating unknown functions that are difficult or costly to evaluate. A popular Bayesian approach to this problem uses a Gaussian process (GP) to construct a posterior distribution over the function of interest given a set of observed measurements, and selects new points to evaluate using the statistics of this posterior. Here we extend these methods to exploit derivative information from the unknown function. We describe methods for Bayesian optimization (BO) and Bayesian quadrature (BQ) in settings where first and second derivatives may be evaluated along with the function itself. We perform sampling-based inference in order to incorporate uncertainty over hyperparameters, and show that both hyperparameter and function uncertainty decrease much more rapidly when using derivative information. Moreover, we introduce techniques for overcoming ill-conditioning issues that have plagued earlier methods for gradient-enhanced Gaussian processes and kriging. We illustrate the efficacy of these methods using applications to real and simulated Bayesian optimization and quadrature problems, and show that exploting derivatives can provide substantial gains over standard methods.

An exciting branch of machine learning research focuses on methods for learning, optimizing, and integrating unknown functions that are difficult or costly to evaluate. A popular Bayesian approach to this problem uses a Gaussian process (GP) to construct a posterior distribution over the function of interest given a set of observed measurements, and selects new points to evaluate using the statistics of this posterior. Here we extend these methods to exploit derivative information from the unknown function. We describe methods for Bayesian optimization (BO) and Bayesian quadrature (BQ) in settings where first and second derivatives may be evaluated along with the function itself. We perform sampling-based inference in order to incorporate uncertainty over hyperparameters, and show that both hyperparameter and function uncertainty decrease much more rapidly when using derivative information. Moreover, we introduce techniques for overcoming ill-conditioning issues that have plagued earlier methods for gradient-enhanced Gaussian processes and kriging. We illustrate the efficacy of these methods using applications to real and simulated Bayesian optimization and quadrature problems, and show that exploting derivatives can provide substantial gains over standard methods.

This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions, but also for estimating their fitness. The results indicate that fitness inheritance is a promising concept in BOA, because population-sizing requirements for building appropriate models of promising solutions lead to good fitness estimates even if only a small proportion of candidate solutions is evaluated using the actual fitness function. This can lead to a reduction of the number of actual fitness evaluations by a factor of 30 or more.

This paper describes the Georgia Tech team's approach to the CoNLL-2016 supplementary evaluation on discourse relation sense classification. We use long short-term memories (LSTM) to induce distributed representations of each argument, and then combine these representations with surface features in a neural network. The architecture of the neural network is determined by Bayesian hyperparameter search.

Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose a novel Gaussian-process based approach for solving games in this context. We follow a classical Bayesian optimization framework, with sequential sampling decisions based on acquisition functions. Two strategies are proposed, based either on the probability of achieving equilibrium or on the Stepwise Uncertainty Reduction paradigm. Practical and numerical aspects are discussed in order to enhance the scalability and reduce computation time. Our approach is evaluated on several synthetic game problems with varying number of players and decision space dimensions. We show that equilibria can be found reliably for a fraction of the cost (in terms of black-box evaluations) compared to classical, derivative-based algorithms.

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics for comparing the performance of Bayesian optimization methods and propose a ranking mechanism for summarizing performance within various genres or strata of test functions. These test functions serve to mimic the complexity of hyperparameter optimization problems, the most prominent application of Bayesian optimization, but with a closed form which allows for rapid evaluation and more predictable behavior. This offers a flexible and efficient way to investigate functions with specific properties of interest, such as oscillatory behavior or an optimum on the domain boundary.

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard to implement in practice. Also, the existing Bayesian optimization method with exponential convergence requires access to the delta-cover sampling, which was considered to be impractical. Our approach eliminates both requirements and achieves an exponential convergence rate.

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance.

A nonparametric-validated, surrogate approach to optimization has been applied to the computational optimization of eddy-promoter heat exchangers and to the experimental optimization of a multielement airfoil. In addition to the baseline surrogate framework, a surrogate-Pareto framework has been applied to the two-criteria, eddy-promoter design problem. The Pareto analysis improves the predictability of the surrogate results, preserves generality, and provides a means to rapidly determine design trade-offs. Significant contributions have been made in the geometric description used for the eddy-promoter inclusions as well as to the surrogate framework itself. A level-set based, geometric description has been developed to define the shape of the eddy-promoter inclusions. The level-set technique allows for topology changes (from single-body,eddy-promoter configurations to two-body configurations) without requiring any additional logic. The continuity of the output responses for input variations that cross the boundary between topologies has been demonstrated. Input-output continuity is required for the straightforward application of surrogate techniques in which simplified, interpolative models are fitted through a construction set of data. The surrogate framework developed previously has been extended in a number of ways. First, the formulation for a general, two-output, two-performance metric problem is presented. Surrogates are constructed and validated for the outputs. The performance metrics can be functions of both outputs, as well as explicitly of the inputs, and serve to characterize the design preferences. By segregating the outputs and the performance metrics, an additional level of flexibility is provided to the designer. The validated outputs can be used in future design studies and the error estimates provided by the output validation step still apply, and require no additional appeals to the expensive analysis. Second, a candidate-based a posteriori error analysis capability has been developed which provides probabilistic error estimates on the true performance for a design randomly selected near the surrogate-predicted optimal design.

Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue OED for nonlinear systems from a Bayesian perspective, with the goal of choosing experiments that are optimal for parameter inference. Our objective in this context is the expected information gain in model parameters, which in general can only be estimated using Monte Carlo methods. Maximizing this objective thus becomes a stochastic optimization problem. This paper develops gradient-based stochastic optimization methods for the design of experiments on a continuous parameter space. Given a Monte Carlo estimator of expected information gain, we use infinitesimal perturbation analysis to derive gradients of this estimator. We are then able to formulate two gradient-based stochastic optimization approaches: (i) Robbins-Monro stochastic approximation, and (ii) sample average approximation combined with a deterministic quasi-Newton method. A polynomial chaos approximation of the forward model accelerates objective and gradient evaluations in both cases. We discuss the implementation of these optimization methods, then conduct an empirical comparison of their performance. To demonstrate design in a nonlinear setting with partial differential equation forward models, we use the problem of sensor placement for source inversion. Numerical results yield useful guidelines on the choice of algorithm and sample sizes, assess the impact of estimator bias, and quantify tradeoffs of computational cost versus solution quality and robustness.

Bayesian optimization methods allocate limited sampling budgets to maximize expensive-to-evaluate functions. One-step-lookahead policies are often used, but computing optimal multi-step-lookahead policies remains a challenge. We consider a specialized Bayesian optimization problem: finding the superlevel set of an expensive one-dimensional function, with a Markov process prior. We compute the Bayes-optimal sampling policy efficiently, and characterize the suboptimality of one-step lookahead. Our numerical experiments demonstrate that the one-step lookahead policy is close to optimal in this problem, performing within 98% of optimal in the experimental settings considered.

We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic "emulating" statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portfolio analysis using classes of economically and psychologically relevant multi-step ahead portfolio utility functions. Studies with multivariate currency, commodity and stock index time series illustrate the approach and show some of the practical utility and benefits of the Bayesian emulation methodology.

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m x 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Due to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms comprised of mixed optimization techniques. For global optimization, we consider Simulated Annealing (SA), Particle Swarm (PS) and Genetic Algorithm (GA), which rely solely on objective function evaluations; i.e., they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic Implicit Filtering method (IF), which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques combining global optimization and Implicit Filtering address difficulties associated with the non-smooth response, and their performances are shown to significantly decrease the computational time over the global optimization methods alone. To quantify uncertainties associated with the source location and intensity, we employ the Delayed Rejection Adaptive Metropolis (DRAM) and DiffeRential Evolution Adaptive Metropolis (DREAM) algorithms. Marginal densities of the source properties are obtained, and the means of the chains' compare accurately with the estimates produced by the hybrid algorithms.

In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m x 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Due to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms comprised of mixed optimization techniques. For global optimization, we consider Simulated Annealing (SA), Particle Swarm (PS) and Genetic Algorithm (GA), which rely solely on objective function evaluations; i.e., they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic Implicit Filtering method (IF), which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques combining global optimization and Implicit Filtering address difficulties associated with the non-smooth response, and their performances are shown to significantly decrease the computational time over the global optimization methods alone. To quantify uncertainties associated with the source location and intensity, we employ the Delayed Rejection Adaptive Metropolis (DRAM) and DiffeRential Evolution Adaptive Metropolis (DREAM) algorithms. Marginal densities of the source properties are obtained, and the means of the chains' compare accurately with the estimates produced by the hybrid algorithms.

We consider the problem of estimating an RF-device's location based on observations, such as received signal strength, from a set of transmitters with known locations. We survey the literature on this problem, showing that previous authors have considered implicitly or explicitly various metrics. We present a novel Bayesian framework that unifies these works and shows how to optimize the location estimation with respect to a given metric. We demonstrate how the framework can incorporate a general class of algorithms, including both model-based methods and data-driven algorithms such fingerprinting. This is illustrated by re-deriving the most popular algorithms within this framework. When used with a data-driven approach, our framework has cognitive self-improving properties in that it provably improves with increasing data compared to traditional methods. Furthermore, we propose using the error-CDF as a unified way of comparing algorithms based on two methods: (i) stochastic dominance, and (ii) an upper bound on error-CDFs. We prove that an algorithm that optimizes any distance based cost function is not stochastically dominated by any other algorithm. This suggests that in lieu of the search for a universally best localization algorithm, the community should focus on finding the best algorithm for a given well-defined objective.

In this study we will try to answer the following research question: Which neural predictors progress arithmetic performance by means of brain stimulation? A type of machine learning (Bayesian Optimization) will be used in this project together with transcranial alternating current stimulation (tACS). Specific entrainment of oscillations by tACS have been related to cognitive enhancement, i.e. working memory (Jaušovec & Jaušovec, 2014), and perception (Ambrus et al., 2015). Thus, tACS allows direct modulation of brain oscillations that subserve cognitive processes (Dayan, Censor, Buch, Sandrini, & Cohen, 2013), whereby tACS provides an easy tool to causally investigate predictors of numerical skills. Beside these advantages, there are also several limitations of tACS. For instance, the stimulated brain area needs to be verified by combining the design with a neuroimaging technique such as EEG. Moreover, tACS is prone to individual differences such as differences in neuroanatomy, age, and gender (Krause & Cohen Kadosh, 2014). These limitations can be overcome by means of Bayesian Optimization, which is a sampling technique that randomly chooses samples whereby it learns in real-time. This technique is particularly valuable when there is need to explore a large experimental space, which is the case when applying tACS. For instance, it is unclear which stimulation frequency, amplitude, area of stimulation or phase is most advantageous to improve numerical skills since the effects of tACS highly depend on these parameters (Antal & Paulus, 2013; Bergmann, Karabanov, Hartwigsen, Thielscher, & Siebner, 2016). By combining these measurements in one design, monetary and facilitation constraints are evaded since it is not necessary to execute several smaller studies whereby one parameter is manipulated as is currently done in conventional brain stimulation studies. Based upon the results of a Bayesian optimization design, the following step would be to establish a Neuroadaptive Bayesian Optimization design whereby a target brain state is defined that is more efficient and effective in manipulating arithmetic performance (Lorenz et al., 2016).

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.

One of the key challenges facing the professionalservices delivery business is the issue of optimally balancingcompeting demands from multiple, concurrent engagementson a limited supply of skill resources. In this paper, wepresent a framework for combining causal Bayesian analysisand optimization to address this challenge. Our frameworkintegrates the identification and modeling of the impact ofvarious staffing factors on the delivery quality of individualengagements, and the optimization of the collective adjustmentsof these staffing factors, to maximize overall delivery qualityfor a pool of engagements. We describe a prototype systembuilt using this framework and actual services delivery datafrom IBM’s IT consulting business. System evaluation underrealistic scenarios constructed using historical delivery recordsprovides encouraging evidence that this framework can lead tosignificant delivery quality improvements. These initial resultsfurther open up exciting opportunities of additional future workin this area, including the integration of temporal relationshipsfor causal learning and multi-period optimization to addressmore complex business scenarios. ©2009 Microsoft Corporation. All rights reserved.

亚洲计算机图形学协会的在线研讨会 Asiagraphics Web Seminar (AG Webinar) 研讨会的详细信息及直播时间可查看AG Webinar的主页： http://www.asiagraphics.org/webinar/ Asiagraphics主页：http://www.asiagraphics.org 更多计算机图形学相关资源可查看： GAMES主页：http://games-cn.org

In this paper, we present the application of a recently developed algorithm for Bayesian multi-objective optimization to the design of a commercial aircraft environment control system (ECS). In our model, the ECS is composed of two cross-flow heat exchangers, a centrifugal compressor and a radial turbine, the geometries of which are simultaneously optimized to achieve minimal weight and entropy generation of the system. While both objectives impact the overall performance of the aircraft, they are shown to be antagonistic and a set of trade-off design solutions is identified. The algorithm used for optimizing the system implements a Bayesian approach to the multi-objective optimization problem in the presence of non-linear constraints and the emphasis is on conducting the optimization using a limited number of system simulations. Noteworthy features of this particular application include a non-hypercubic design domain and the presence of hidden constraints due to simulation failures.

Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm that, based on the current state, dynamically switches between a sequential policy and a batch policy with variable batch sizes. We provide theoretical justification for our algorithm and present experimental results on eight benchmark BO problems. The results show that our method achieves substantial speedup (up to %78) compared to a pure sequential policy, without suffering any significant performance loss.

Search and Detection Theory is the overarching field of study that covers many scenarios. These range from simple search and rescue acts to prosecuting aerial/surface/submersible targets on mission. This research looks at varying the known discrete and Bayesian algorithm parameters to analyze the optimization. It also expands on previous research of two searchers with search radii coupled to their speed, executing three search patterns: inline spiral search, inline ladder search, and a multipath ladder search. Analysis reveals that the Bayesian search and discrete search work similarly, but the Bayesian search algorithm provides a more useful output in location probability. Results from the continuous search were similar to previous research, but variance in time to detection became more complex than basic increasing or decreasing ranges.

We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger et al. (2007). To accomplish this, we use infinitessimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased. We also show that the stochastic gradient ascent algorithm using the constructed gradient estimator converges to a stationary point of the q-EI surface, and therefore, as the number of multiple starts of the gradient ascent algorithm and the number of steps for each start grow large, the one-step Bayes optimal set of points is recovered. We show in numerical experiments that our method for maximizing the q-EI is faster than methods based on closed-form evaluation using high-dimensional integration, when considering many parallel function evaluations, and is comparable in speed when considering few. We also show that the resulting one-step Bayes optimal algorithm for parallel global optimization finds high quality solutions with fewer evaluations that a heuristic based on approximately maximizing the q-EI. A high quality open source implementation of this algorithm is available in the open source Metrics Optimization Engine (MOE).

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness of Bayesian optimization. Although Gaussian processes provide a flexible prior over functions which can be queried efficiently, there are various classes of functions that remain difficult to model. One of the most frequently occurring of these is the class of non-stationary functions. The optimization of the hyperparameters of machine learning algorithms is a problem domain in which parameters are often manually transformed a priori, for example by optimizing in "log-space," to mitigate the effects of spatially-varying length scale. We develop a methodology for automatically learning a wide family of bijective transformations or warpings of the input space using the Beta cumulative distribution function. We further extend the warping framework to multi-task Bayesian optimization so that multiple tasks can be warped into a jointly stationary space. On a set of challenging benchmark optimization tasks, we observe that the inclusion of warping greatly improves on the state-of-the-art, producing better results faster and more reliably.