Historically, design and analysis of computer experiments focused on deterministic solvers from the physical sciences via Gaussian process (GP) interpolation. But nowadays computer modeling is common in the social, management and biological sciences, where stochastic simulations abound. In this minisymposium, we bring together a selection of researchers in the areas of statistical surrogate modeling, active learning, and Bayesian optimization of stochastic computer model, simulation campaigns, and high volume observational studies. Noisier simulations demand bigger experiments to isolate signal from noise, and more sophisticated GP models -- such as adding a variance processes to track changes in noise throughout the input space in the face of heteroskedasticity. Appropriate surrogate modeling is key to the propagation of uncertainty to decision criteria underlying important large-scale and real time control of systems which rely on expensive simulation campaigns. Think of synthesis between off-line simulation of urban road traffic and ride demand with on-line measurements from potential riders and their routes in the assignment of a car. Or similarly the combination of limited data on disease spread combined with social-network backed simulation of epidemiological dynamics and entertainment of intervention strategies such as vaccination and quarantine. The talks will be on these methodologies and applied in those challenging modeling and optimization real-world problems.
16:30
Quantile-based Gaussian Process Emulation for a Stochastic Agent Based Model
Arindam Fadikar | Argonne National Lab | United States
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Arindam Fadikar | Argonne National Lab | United States
In a number of cases, the Quantile Gaussian Process (QGP) has proven effective in emulating stochastic, univariate computer model output (Plumlee and Tuo, 2014). Based on quantile GP, we develop an approach that models
output from a stochastic computer model and handles both uni-variate and multi-variate responses. Our motivating example is taken from a computer model which simulates the Ebola epidemic in West Africa (2014) producing a time series of the count of infected individuals. The basic modeling approach is adapted from Higdon et al. (2008) which uses a basis representation to capture the multivariate model output. The QGP surrogate is then used in a Bayesian calibration setup for producing future disease characteristics.
17:00
Efficient optimization of high-dimensional expensive functions
Matthias Poloczek | Uber | United States
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Matthias Poloczek | Uber | United States
Bayesian optimization (BO) has recently emerged as powerful technique for the global optimization of expensive-to-evaluate black-box functions. However, BO's performance often degenerates for higher dimensional problems (with say more than 15 dimensions), as they arise in robotics, reinforcement learning, scientific problems, or network architecture search. The main reasons are that the commonly used Gaussian process surrogate models struggle with the heterogeneity of high-dimensional search domains and that inherent uncertainty leads current acquisition functions to over-explore. Thus, it is not surprising that expanding BO to higher-dimensional search spaces is widely acknowledged as one of the most important goals in the field. In this talk I will present a novel optimization algorithm for high-dimensional problems and present experimental results that demonstrate that it outperforms the state-of-the-art on a variety of benchmarks.
17:30
A Differentiable Programming Approach to Bayesian Optimization
Max Balandat | Facebook | United States
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Max Balandat | Facebook | United States
Bayesian Optimization is an established methodology for optimizing expensive-to-evaluate black-box functions, which is applied to a wide variety of problems, including machine learning hyperparameter optimization, A/B testing, robotics, and other engineering problems. In some domains the observations gathered from the underlying process are subject to significant noise, e.g. in A/B tests, stochastic simulations, or problems involving complex manufacturing processes. This observation noise is often heteroskedastic in nature. In addition, many of these domains may also benefit from or even require a high number of parallel evaluations, e.g. because of stationarity concerns (A/B tests) or cost efficiency reasons (involving a high fixed cost, e.g. in manufacturing). In this talk, we introduce novel formulations of parallel Noisy Expected Improvement and the parallel Knowledge Gradient, acquisition functions for Bayesian Optimization designed to exploit advances in modern computing, specifically highly parallelized and hardware-accelerated differentiable programming. We couple these with new, flexible, easy-to-implement heteroskedastic GP models in order to achieve highly effective Bayesian Optimization in noisy, parallel evaluation settings. We show how dependencies of the observation noise on auxiliary fidelity parameters (either modeled or known, e.g sample sizes) can be used to jointly optimize fidelity and basic parameters in order to maximize efficiency.
18:00
Bayesian Optimization and Dimension Reduction with Active Subspaces
Mickael Binois | INRA Sophia Antipolis Mediterranean | France
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Mickael Binois | INRA Sophia Antipolis Mediterranean | France
Black-box problems, with no available derivatives, possibly noisy, and expensive to evaluate are a common occurrence. Bayesian Optimization (BO) showed its efficiency in such setups, but generally for a moderate number of variables. To scale BO with high-dimensional parameter spaces, we present a Gaussian process (GP) based methodology that incorporates active subspace estimation. The latter identifies the most influential directions in the original domain. Here, we show that the active subspace of a GP as well as its update with new designs can be expressed directly. It thus enables a sequential uncertainty reduction strategy balancing dimension reduction and optimization goals. We discuss relations with existing methods from the literature and present results on several examples.