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Design is an inseparable part of most scientific and engineering tasks, including real and simulation-based experimental design processes and parameter/hyperparameter tuning/optimization. Several model-based experimental design techniques have been developed for design in domains with partial available knowledge about the underlying process. This article focuses on a powerful class of model-based experimental design called the mean objective cost of uncertainty (MOCU). The MOCU-based techniques are objective-based, meaning that they take the main objective of the process into account during the experimental design process. However, the lack of scalability of MOCU-based techniques prevents their application to most practical problems, including large discrete or combinatorial spaces. To achieve a scalable objective-based experimental design, this article proposes a graph-based MOCU-based Bayesian optimization framework. The correlations among samples in the large design space are accounted for using a graph-based Gaussian process, and an efficient closed-form sequential selection is achieved through the well-known expected improvement policy. The proposed framework's performance is assessed through the structural intervention in gene regulatory networks, aiming to make the network away from the states associated with cancer.

State-space models (SSMs) are a rich class of dynamical models with a wide range of applications in economics, healthcare, computational biology, robotics, and more. Proper analysis, control, learning, and decision-making in dynamical systems modeled by SSMs depend on the accuracy of the inferred/learned model. Most of the existing inference techniques for SSMs are capable of dealing with very small systems, unable to be applied to most of the large-scale practical problems. Toward this, this article introduces a two-stage Bayesian optimization (BO) framework for scalable and efficient inference in SSMs. The proposed framework maps the original large parameter space to a reduced space, containing a small linear combination of the original space. This reduced space, which captures the most variability in the inference function (e.g., log likelihood or log a posteriori), is obtained by eigenvalue decomposition of the covariance of gradients of the inference function approximated by a particle filtering scheme. Then, an exponential reduction in the search space of parameters during the inference process is achieved through the proposed two-stage BO policy, where the solution of the first-stage BO policy in the reduced space specifies the search space of the second-stage BO in the original space. The proposed framework's accuracy and speed are demonstrated through several experiments, including real metagenomics data from a gut microbial community.

Data in many practical problems are acquired according to decisions or actions made by users or experts to achieve specific goals. For instance, policies in the mind of biologists during the intervention process in genomics and metagenomics are often reflected in available data in these domains, or data in cyber-physical systems are often acquired according to actions/decisions made by experts/engineers for purposes, such as control or stabilization. Quantification of experts' policies through available data, which is also known as reward function learning, has been discussed extensively in the literature in the context of inverse reinforcement learning (IRL). However, most of the available techniques come short to deal with practical problems due to the following main reasons: 1) lack of scalability: arising from incapability or poor performance of existing techniques in dealing with large systems and 2) lack of reliability: coming from the incapability of the existing techniques to properly learn the optimal reward function during the learning process. Toward this, in this brief, we propose a multifidelity Bayesian optimization (MFBO) framework that significantly scales the learning process of a wide range of existing IRL techniques. The proposed framework enables the incorporation of multiple approximators and efficiently takes their uncertainty and computational costs into account to balance exploration and exploitation during the learning process. The proposed framework's high performance is demonstrated through genomics, metagenomics, and sets of random simulated problems.