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A tutorial on the informativity framework for data-driven control

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A tutorial on the informativity framework for data-driven co...

IEEE Conference on Decision and Control

作者： Henk J. van Waarde J. Eising M. Kanat Camlibel Harry L. Trentelman Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Groningen Netherlands Department of Mechanical and Aerospace Engineering UC San Diego USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

The purpose of this paper is to provide a tutorial on the so-called informativity framework for direct data-driven control. This framework views data-driven analysis and design through the lens of robust control, and aims at assessing system properties and determining controllers for sets of systems unfalsified by the data. We will first introduce the informativity approach at an abstract level. Thereafter, we will study several case studies where we highlight the strength of the approach in the context of stabilizability analysis and stabilizing feedback design in different setups involving exact and noisy data, and for both input-state and input-output measurements. Finally, we provide an account of other applications of the data informativity framework.

关键词： Robust control Tutorials Noise measurement Lenses

QUADRATIC MATRIX INEQUALITIES WITH APPLICATIONS TO DATA-BASED CONTROL

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arXiv 2022年

作者： van Waarde, Henk J. Camlibel, M. Kanat Eising, Jaap Trentelman, Harry L. Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Netherlands Department of Mechanical and Aerospace Engineering UC San Diego United States

This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, bounded, or has nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma, that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMI's can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller, and also leads to explicit formulas for data-guided feedback gains. Copyright © 2022, The Authors. All rights reserved.

关键词： Robust control

Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features

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arXiv 2022年

作者： Radhakrishnan, Adityanarayanan Beaglehole, Daniel Pandit, Parthe Belkin, Mikhail Massachusetts Institute of Technology United States Broad Institute of MIT and Harvard United States Halıcıoğlu Data Science Institute UC San Diego United States Computer Science and Engineering UC San Diego United States

In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear. Identifying such a mechanism is key to advancing performance and interpretability of neural networks and promoting reliable adoption of these models in scientific applications. In this paper, we identify and characterize the mechanism through which deep fully connected neural networks learn features. We posit the Deep Neural Feature Ansatz, which states that neural feature learning occurs by implementing the average gradient outer product to up-weight features strongly related to model output. Our ansatz sheds light on various deep learning phenomena including emergence of spurious features and simplicity biases and how pruning networks can increase performance, the "lottery ticket hypothesis." Moreover, the mechanism identified in our work leads to a backpropagation-free method for feature learning with any machine learning model. To demonstrate the effectiveness of this feature learning mechanism, we use it to enable feature learning in classical, non-feature learning models known as kernel machines and show that the resulting models, which we refer to as Recursive Feature Machines, achieve state-of-the-art performance on tabular data. © 2022, CC BY.

关键词： Deep neural networks

Estimating Total Treatment Effect in Randomized Experiments with Unknown Network Structure

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arXiv 2022年

作者： Yu, Christina Lee Airoldi, Edoardo M. Borgs, Christian Chayes, Jennifer T. School of Operations Research and Information Engineering Cornell University IthacaNY United States Department of Statistics Operations and Data Science Fox School of Business Temple University PhiladelphiaPA United States Department of Electrical Engineering and Computer Science UC Berkeley BerkeleyCA United States Departments of Electrical Engineering and Computer Science Statistics Mathematics The School of Information UC Berkeley BerkeleyCA United States

Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, to public policy and to the technology industry at large. Here, we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact their neighbors’ outcomes, an issue referred to as network interference or as non-individualized treatment response. A key challenge in these situations, is that the network is often unknown, and difficult, or costly, to measure. In this paper, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference, assuming a potential outcomes model with heterogeneous additive network effects. This model encompasses a broad class of network interference sources, including spillover, peer effects, and contagion. Within this framework, we show that, surprisingly, given access to average historical baseline measurements prior to the experiment, we can develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. We believe our results are poised to impact current randomized experimentation strategies due to its ease of interpretation and implementation, alongside its provable theoretical insights under heterogeneous network effects. Copyright © 2022, The Authors. All rights reserved.

关键词： Heterogeneous networks

A behavioral approach to data-driven control with noisy input-output data

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arXiv 2022年

作者： van Waarde, Henk J. Eising, Jaap Camlibel, M. Kanat Trentelman, Harry L. Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Netherlands Department of Mechanical and Aerospace Engineering UC San Diego United States

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich’s S-lemma. Copyright © 2022, The Authors. All rights reserved.

关键词： Matrix algebra

On the Computational Complexity of Schrödinger Operators

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arXiv 2024年

作者： Zheng, Yufan Leng, Jiaqi Liu, Yizhou Wu, Xiaodi Department of Computer Science University of Maryland United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Simons Institute for the Theory of Computing Department of Mathematics UC Berkeley United States Physics of Living Systems Department of Physics MIT United States Department of Mechanical Engineering MIT United States

We study computational problems related to the Schrödinger operator H = −∆ + V in the real space under the condition that (i) the potential function V is smooth and has its value and derivative bounded within some polynomial of n and (ii) V only consists of O(1)-body interactions. We prove that (i) simulating the dynamics generated by the Schrödinger operator implements universal quantum computation, i.e., it is BQP-hard, and (ii) estimating the ground energy of the Schrödinger operator is as hard as estimating that of local Hamiltonians with no sign problem (a.k.a. stoquastic Hamiltonians), i.e., it is StoqMA-complete. This result is particularly intriguing because the ground energy problem for general bosonic Hamiltonians is known to be QMA-hard and it is widely believed that StoqMA (Equation presented) QMA. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Addressable Superconductor Integrated Circuit Memory from Delay Lines

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arXiv 2022年

作者： Volk, Jennifer Wynn, Alex Sherwood, Timothy Tzimpragos, Georgios UC Santa Barbara Department of Electrical and Computer Engineering Santa BarbaraCA93106 United States Massachusetts Institute of Technology Lincoln Laboratory LexingtonMA02420 United States UC Santa Barbara Department of Computer Science Santa BarbaraCA93106 United States University of Michigan Department of Electrical Engineering and Computer Science Ann ArborMI48109 United States

Recent advances in logic schemes and fabrication processes have renewed interest in using superconductor electronics for energy-efficient computing and quantum control processors. However, scalable superconducting memory still poses a challenge. To address this issue, we present an alternative to approaches that solely emphasize storage cell miniaturization by exploiting the minimal attenuation and dispersion properties of superconducting passive transmission lines to develop a delay-line memory system. This fully superconducting design operates at speeds between 20 GHz and 100 GHz, with ±24% and ±13% bias margins, respectively, and demonstrates data densities in the 10s of Mbit/cm2 with the MIT Lincoln Laboratory SC2 fabrication process. Additionally, the circulating nature of this design allows for minimal control circuitry, eliminates the need for data splitting and merging, and enables inexpensive implementations of sequential access and content-addressable memories. Further advances in fabrication processes suggest data densities of 100s of Mbit/cm2 and beyond. © 2022, CC BY.

关键词： Timing circuits

Ready policy one: World building through active learning 37

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Ready policy one: World building through active learning

37th International Conference on Machine Learning, ICML 2020

作者： Ball, Philip J. Holder, Jack Parker Pacchiano, Aldo Choromanski, Krzysztof Roberts, Stephen Department of Engineering Science University of Oxford Department of Electrical Engineering and Computer Sciences Uc Berkeley Google Brain Robotics

ISBN: (纸本)9781713821120

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v.s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches. © ICML 2020. All rights reserved.

关键词： Heuristic methods

Improving conditional coverage via orthogonal quantile regression 21

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Improving conditional coverage via orthogonal quantile regre...

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Shai Feldman Stephen Bates Yaniv Romano Department of Computer Science Technion Israel Departments of Statistics and of EECS UC Berkeley Departments of Electrical and Computer Engineering and of Computer Science Technion Israel

ISBN: (纸本)9781713845393

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression—it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.

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