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This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The…

Optimization and Control · Mathematics 2021-10-08 Dominik Garmatter , Margherita Porcelli , Francesco Rinaldi , Martin Stoll

In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have…

Machine Learning · Computer Science 2019-06-11 Michał Dereziński , Feynman Liang , Michael W. Mahoney

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected…

Machine Learning · Statistics 2020-01-15 Adam Foster , Martin Jankowiak , Eli Bingham , Paul Horsfall , Yee Whye Teh , Tom Rainforth , Noah Goodman

Within the field of optimal experimental design, \emph{sensor placement} refers to the act of finding the optimal locations of data collecting sensors, with the aim to optimise reconstruction of an unknown parameter from finite data. In…

Optimization and Control · Mathematics 2025-09-26 Christian Aarset , Tram Thi Ngoc Nguyen

In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…

Statistics Theory · Mathematics 2025-05-02 Phuoc-Truong Huynh

We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the…

Optimization and Control · Mathematics 2016-04-20 Seong Jun Kim , Sung Ha Kang , Haomin Zhou

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

Applications · Statistics 2022-03-23 Jan Povala , Ieva Kazlauskaite , Eky Febrianto , Fehmi Cirak , Mark Girolami

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…

Machine Learning · Statistics 2017-11-15 Zeyuan Allen-Zhu , Yuanzhi Li , Aarti Singh , Yining Wang

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

Optimization and Control · Mathematics 2019-05-20 Matthew J. Zahr , Kevin T. Carlberg , Drew P. Kouri

This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search…

Optimization and Control · Mathematics 2024-12-20 A. Batou

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

Numerical Analysis · Mathematics 2025-10-30 James V. Roggeveen , Michael P. Brenner

Most computational approaches to Bayesian experimental design require making posterior calculations repeatedly for a large number of potential designs and/or simulated datasets. This can be expensive and prohibit scaling up these methods to…

Computation · Statistics 2021-11-18 Dennis Prangle , Sophie Harbisher , Colin S Gillespie

In this work, the Bayesian approach to inverse problems is formulated in an all-at-once setting. The advantages of the all-at-once formulation are known to include the avoidance of a parameter-to-state map as well as numerical improvements,…

Numerical Analysis · Mathematics 2021-01-15 Anna Schlintl , Barbara Kaltenbacher

Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget…

Machine Learning · Statistics 2026-05-27 Yujia Guo , Daolang Huang , Xinyu Zhang , Sammie Katt , Samuel Kaski , Ayush Bharti

In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…

Numerical Analysis · Mathematics 2018-07-04 Lingling Ma , Qiuqi Li , Lijian Jiang

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…

Machine Learning · Computer Science 2021-03-16 Jiaxin Zhang , Sirui Bi , Guannan Zhang

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…

Machine Learning · Statistics 2020-08-17 Steven Kleinegesse , Michael U. Gutmann

We study the problem of causal structure learning over a set of random variables when the experimenter is allowed to perform at most $M$ experiments in a non-adaptive manner. We consider the optimal learning strategy in terms of minimizing…

Machine Learning · Computer Science 2017-03-01 AmirEmad Ghassami , Saber Salehkaleybar , Negar Kiyavash

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

Methodology · Statistics 2017-02-07 Antony M. Overstall , James M. McGree , Christopher C. Drovandi

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Optimization and Control · Mathematics 2023-01-13 Emiland Garrabe , Giovanni Russo