This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

This survey presents recent research on determining control-theoretic properties and
designing controllers with rigorous guarantees using semidefinite programming and for …

Bayesian Optimization (BO), the application of Bayesian function approximation to finding
optima of expensive functions, has exploded in popularity in recent years. In particular, much …

Consider the sequential optimization of an expensive to evaluate and possibly non-convex
objective function $ f $ from noisy feedback, that can be considered as a continuum-armed …

Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations
have been developed to simulate molecular systems, where an explicit description of …

We address the consistency of a kernel ridge regression estimate of the conditional mean
embedding (CME), which is an embedding of the conditional distribution of $ Y $ given $ X …

Gaussian process regression is a popular Bayesian framework for surrogate modeling of
expensive data sources. As part of a broader effort in scientific machine learning, many …

Data-driven models are subject to model errors due to limited and noisy training data. Key to
the application of such models in safety-critical domains is the quantification of their model …

Bayesian optimization is known to be difficult to scale to high dimensions, because the
acquisition step requires solving a non-convex optimization problem in the same search …

Three major challenges in reinforcement learning are the complex dynamical systems with
large state spaces, the costly data acquisition processes, and the deviation of real-world …