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2019


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Controlling Heterogeneous Stochastic Growth Processes on Lattices with Limited Resources

Haksar, R., Solowjow, F., Trimpe, S., Schwager, M.

In Proceedings of the 58th IEEE International Conference on Decision and Control (CDC) , 58th IEEE International Conference on Decision and Control (CDC), December 2019 (proceedings) Accepted

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PDF [BibTex]

2019


PDF [BibTex]


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A Learnable Safety Measure

Heim, S., Rohr, A. V., Trimpe, S., Badri-Spröwitz, A.

Conference on Robot Learning, November 2019 (conference) Accepted

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Arxiv [BibTex]

Arxiv [BibTex]


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Fast Feedback Control over Multi-hop Wireless Networks with Mode Changes and Stability Guarantees

Baumann, D., Mager, F., Jacob, R., Thiele, L., Zimmerling, M., Trimpe, S.

ACM Transactions on Cyber-Physical Systems, 4(2):18, November 2019 (article)

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arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]


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Predictive Triggering for Distributed Control of Resource Constrained Multi-agent Systems

Mastrangelo, J. M., Baumann, D., Trimpe, S.

In Proceedings of the 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems, 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys), September 2019 (inproceedings)

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Event-triggered Pulse Control with Model Learning (if Necessary)

Baumann, D., Solowjow, F., Johansson, K. H., Trimpe, S.

In Proceedings of the American Control Conference, pages: 792-797, American Control Conference (ACC), July 2019 (inproceedings)

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Data-driven inference of passivity properties via Gaussian process optimization

Romer, A., Trimpe, S., Allgöwer, F.

In Proceedings of the European Control Conference, European Control Conference (ECC), June 2019 (inproceedings)

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PDF [BibTex]

PDF [BibTex]


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Actively Learning Gaussian Process Dynamics

Buisson-Fenet, M., Solowjow, F., Trimpe, S.

2019 (techreport) Submitted

Abstract
Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage information-theoretical properties arising naturally during Gaussian process regression, while respecting constraints on the sampling process imposed by the system dynamics. Sample points are selected in regions with high uncertainty, leading to exploratory behavior and data-efficient training of the model. All results are verified in an extensive numerical benchmark.

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ArXiv [BibTex]


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Trajectory-Based Off-Policy Deep Reinforcement Learning

Doerr, A., Volpp, M., Toussaint, M., Trimpe, S., Daniel, C.

In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), June 2019 (inproceedings)

Abstract
Policy gradient methods are powerful reinforcement learning algorithms and have been demonstrated to solve many complex tasks. However, these methods are also data-inefficient, afflicted with high variance gradient estimates, and frequently get stuck in local optima. This work addresses these weaknesses by combining recent improvements in the reuse of off-policy data and exploration in parameter space with deterministic behavioral policies. The resulting objective is amenable to standard neural network optimization strategies like stochastic gradient descent or stochastic gradient Hamiltonian Monte Carlo. Incorporation of previous rollouts via importance sampling greatly improves data-efficiency, whilst stochastic optimization schemes facilitate the escape from local optima. We evaluate the proposed approach on a series of continuous control benchmark tasks. The results show that the proposed algorithm is able to successfully and reliably learn solutions using fewer system interactions than standard policy gradient methods.

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Resource-aware IoT Control: Saving Communication through Predictive Triggering

Trimpe, S., Baumann, D.

IEEE Internet of Things Journal, 6(3):5013-5028, June 2019 (article)

Abstract
The Internet of Things (IoT) interconnects multiple physical devices in large-scale networks. When the 'things' coordinate decisions and act collectively on shared information, feedback is introduced between them. Multiple feedback loops are thus closed over a shared, general-purpose network. Traditional feedback control is unsuitable for design of IoT control because it relies on high-rate periodic communication and is ignorant of the shared network resource. Therefore, recent event-based estimation methods are applied herein for resource-aware IoT control allowing agents to decide online whether communication with other agents is needed, or not. While this can reduce network traffic significantly, a severe limitation of typical event-based approaches is the need for instantaneous triggering decisions that leave no time to reallocate freed resources (e.g., communication slots), which hence remain unused. To address this problem, novel predictive and self triggering protocols are proposed herein. From a unified Bayesian decision framework, two schemes are developed: self triggers that predict, at the current triggering instant, the next one; and predictive triggers that check at every time step, whether communication will be needed at a given prediction horizon. The suitability of these triggers for feedback control is demonstrated in hardware experiments on a cart-pole, and scalability is discussed with a multi-vehicle simulation.

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PDF arXiv DOI [BibTex]

PDF arXiv DOI [BibTex]


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DeepOBS: A Deep Learning Optimizer Benchmark Suite

Schneider, F., Balles, L., Hennig, P.

7th International Conference on Learning Representations (ICLR), May 2019 (conference)

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link (url) [BibTex]

link (url) [BibTex]


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Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop Networks

(Best Paper Award)

Mager, F., Baumann, D., Jacob, R., Thiele, L., Trimpe, S., Zimmerling, M.

In Proceedings of the 10th ACM/IEEE International Conference on Cyber-Physical Systems, pages: 97-108, 10th ACM/IEEE International Conference on Cyber-Physical Systems, April 2019 (inproceedings)

Abstract
Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals below 100 ms. Low-power wireless is preferred for its flexibility, low cost, and small form factor, especially if the devices support multi-hop communication. Thus far, however, closed-loop control over multi-hop low-power wireless has only been demonstrated for update intervals on the order of multiple seconds. This paper presents a wireless embedded system that tames imperfections impairing control performance such as jitter or packet loss, and a control design that exploits the essential properties of this system to provably guarantee closed-loop stability for linear dynamic systems. Using experiments on a testbed with multiple cart-pole systems, we are the first to demonstrate the feasibility and to assess the performance of closed-loop control and coordination over multi-hop low-power wireless for update intervals from 20 ms to 50 ms.

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Demo Abstract: Fast Feedback Control and Coordination with Mode Changes for Wireless Cyber-Physical Systems

(Best Demo Award)

Mager, F., Baumann, D., Jacob, R., Thiele, L., Trimpe, S., Zimmerling, M.

Proceedings of the 18th ACM/IEEE Conference on Information Processing in Sensor Networks (IPSN), pages: 340-341, 18th ACM/IEEE Conference on Information Processing in Sensor Networks (IPSN), April 2019 (poster)

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arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]


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Fast and Robust Shortest Paths on Manifolds Learned from Data

Arvanitidis, G., Hauberg, S., Hennig, P., Schober, M.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1506-1515, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization

de Roos, F., Hennig, P.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1448-1457, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

Abstract
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dominate contemporary machine learning, however, this approach is not readily available. We propose an iterative algorithm inspired by classic iterative linear solvers that uses a probabilistic model to actively infer a pre-conditioner in situations where Hessian-projections can only be constructed with strong Gaussian noise. The algorithm is empirically demonstrated to efficiently construct effective pre-conditioners for stochastic gradient descent and its variants. Experiments on problems of comparably low dimensionality show improved convergence. In very high-dimensional problems, such as those encountered in deep learning, the pre-conditioner effectively becomes an automatic learning-rate adaptation scheme, which we also empirically show to work well.

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Fast and Resource-Efficient Control of Wireless Cyber-Physical Systems

Baumann, D.

KTH Royal Institute of Technology, Stockholm, Febuary 2019 (phdthesis)

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PDF [BibTex]

PDF [BibTex]


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Data-efficient Auto-tuning with Bayesian Optimization: An Industrial Control Study

Neumann-Brosig, M., Marco, A., Schwarzmann, D., Trimpe, S.

IEEE Transactions on Control Systems Technology, 2019 (article) Accepted

Abstract
Bayesian optimization is proposed for automatic learning of optimal controller parameters from experimental data. A probabilistic description (a Gaussian process) is used to model the unknown function from controller parameters to a user-defined cost. The probabilistic model is updated with data, which is obtained by testing a set of parameters on the physical system and evaluating the cost. In order to learn fast, the Bayesian optimization algorithm selects the next parameters to evaluate in a systematic way, for example, by maximizing information gain about the optimum. The algorithm thus iteratively finds the globally optimal parameters with only few experiments. Taking throttle valve control as a representative industrial control example, the proposed auto-tuning method is shown to outperform manual calibration: it consistently achieves better performance with a low number of experiments. The proposed auto-tuning framework is flexible and can handle different control structures and objectives.

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arXiv (PDF) DOI Project Page [BibTex]

arXiv (PDF) DOI Project Page [BibTex]


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Event-triggered Learning

Solowjow, F., Trimpe, S.

2019 (techreport) Submitted

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arXiv PDF [BibTex]


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Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I. C. F., Hennig, P.

Statistics and Computing, 2019 (article) Accepted

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link (url) [BibTex]

link (url) [BibTex]


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Actively Learning Dynamical Systems with Gaussian Processes

Buisson-Fenet, M.

Mines ParisTech, PSL Research University, 2019 (mastersthesis)

Abstract
Predicting the behavior of complex systems is of great importance in many fields such as engineering, economics or meteorology. The evolution of such systems often follows a certain structure, which can be induced, for example from the laws of physics or of market forces. Mathematically, this structure is often captured by differential equations. The internal functional dependencies, however, are usually unknown. Hence, using machine learning approaches that recreate this structure directly from data is a promising alternative to designing physics-based models. In particular, for high dimensional systems with nonlinear effects, this can be a challenging task. Learning dynamical systems is different from the classical machine learning tasks, such as image processing, and necessitates different tools. Indeed, dynamical systems can be actuated, often by applying torques or voltages. Hence, the user has a power of decision over the system, and can drive it to certain states by going through the dynamics. Actuating this system generates data, from which a machine learning model of the dynamics can be trained. However, gathering informative data that is representative of the whole state space remains a challenging task. The question of active learning then becomes important: which control inputs should be chosen by the user so that the data generated during an experiment is informative, and enables efficient training of the dynamics model? In this context, Gaussian processes can be a useful framework for approximating system dynamics. Indeed, they perform well on small and medium sized data sets, as opposed to most other machine learning frameworks. This is particularly important considering data is often costly to generate and process, most of all when producing it involves actuating a complex physical system. Gaussian processes also yield a notion of uncertainty, which indicates how sure the model is about its predictions. In this work, we investigate in a principled way how to actively learn dynamical systems, by selecting control inputs that generate informative data. We model the system dynamics by a Gaussian process, and use information-theoretic criteria to identify control trajectories that maximize the information gain. Thus, the input space can be explored efficiently, leading to a data-efficient training of the model. We propose several methods, investigate their theoretical properties and compare them extensively in a numerical benchmark. The final method proves to be efficient at generating informative data. Thus, it yields the lowest prediction error with the same amount of samples on most benchmark systems. We propose several variants of this method, allowing the user to trade off computations with prediction accuracy, and show it is versatile enough to take additional objectives into account.

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[BibTex]

[BibTex]

2016


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A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Garcia Cifuentes, C., Kappler, D., Schaal, S.

The International Journal of Robotics Research, 35(14):1731-1749, December 2016 (article)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. The GF represents the belief of the current state by a Gaussian distribution, whose mean is an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF as the solution to a constrained optimization problem. From this new perspective, the GF is seen as a special case of a much broader class of filters, obtained by relaxing the constraint on the form of the approximate posterior. On this basis, we outline some conditions which potential generalizations have to satisfy in order to maintain the computational efficiency of the GF. We propose one concrete generalization which corresponds to the standard GF using a pseudo measurement instead of the actual measurement. Extending an existing GF implementation in this manner is trivial. Nevertheless, we show that this small change can have a major impact on the estimation accuracy.

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PDF DOI Project Page [BibTex]

2016


PDF DOI Project Page [BibTex]


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Predictive and Self Triggering for Event-based State Estimation

Trimpe, S.

In Proceedings of the 55th IEEE Conference on Decision and Control (CDC), pages: 3098-3105, Las Vegas, NV, USA, December 2016 (inproceedings)

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Robust Gaussian Filtering using a Pseudo Measurement

Wüthrich, M., Garcia Cifuentes, C., Trimpe, S., Meier, F., Bohg, J., Issac, J., Schaal, S.

In Proceedings of the American Control Conference (ACC), Boston, MA, USA, July 2016 (inproceedings)

Abstract
Most widely-used state estimation algorithms, such as the Extended Kalman Filter and the Unscented Kalman Filter, belong to the family of Gaussian Filters (GF). Unfortunately, GFs fail if the measurement process is modelled by a fat-tailed distribution. This is a severe limitation, because thin-tailed measurement models, such as the analytically-convenient and therefore widely-used Gaussian distribution, are sensitive to outliers. In this paper, we show that mapping the measurements into a specific feature space enables any existing GF algorithm to work with fat-tailed measurement models. We find a feature function which is optimal under certain conditions. Simulation results show that the proposed method allows for robust filtering in both linear and nonlinear systems with measurements contaminated by fat-tailed noise.

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Web link (url) DOI Project Page [BibTex]

Web link (url) DOI Project Page [BibTex]


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Active Uncertainty Calibration in Bayesian ODE Solvers

Kersting, H., Hennig, P.

Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI), pages: 309-318, (Editors: Ihler, A. and Janzing, D.), AUAI Press, June 2016 (conference)

Abstract
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al.~introduced a sampling-based class of methods that are `well-calibrated' in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the other hand, Schober et al.~pointed out a precise connection between classic Runge-Kutta ODE solvers and Gaussian filters, which gives only a rough probabilistic calibration, but at negligible cost overhead. By formulating the solution of ODEs as approximate inference in linear Gaussian SDEs, we investigate a range of probabilistic ODE solvers, that bridge the trade-off between computational cost and probabilistic calibration, and identify the inaccurate gradient measurement as the crucial source of uncertainty. We propose the novel filtering-based method Bayesian Quadrature filtering (BQF) which uses Bayesian quadrature to actively learn the imprecision in the gradient measurement by collecting multiple gradient evaluations.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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Automatic LQR Tuning Based on Gaussian Process Global Optimization

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 270-277, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract
This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree- of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four- dimensional tuning problems highlight the method’s potential for automatic controller tuning on robotic platforms.

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Video PDF DOI Project Page [BibTex]

Video PDF DOI Project Page [BibTex]


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Depth-based Object Tracking Using a Robust Gaussian Filter

Issac, J., Wüthrich, M., Garcia Cifuentes, C., Bohg, J., Trimpe, S., Schaal, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2016, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract
We consider the problem of model-based 3D- tracking of objects given dense depth images as input. Two difficulties preclude the application of a standard Gaussian filter to this problem. First of all, depth sensors are characterized by fat-tailed measurement noise. To address this issue, we show how a recently published robustification method for Gaussian filters can be applied to the problem at hand. Thereby, we avoid using heuristic outlier detection methods that simply reject measurements if they do not match the model. Secondly, the computational cost of the standard Gaussian filter is prohibitive due to the high-dimensional measurement, i.e. the depth image. To address this problem, we propose an approximation to reduce the computational complexity of the filter. In quantitative experiments on real data we show how our method clearly outperforms the standard Gaussian filter. Furthermore, we compare its performance to a particle-filter-based tracking method, and observe comparable computational efficiency and improved accuracy and smoothness of the estimates.

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Video Bayesian Object Tracking Library Bayesian Filtering Framework Object Tracking Dataset link (url) DOI Project Page [BibTex]

Video Bayesian Object Tracking Library Bayesian Filtering Framework Object Tracking Dataset link (url) DOI Project Page [BibTex]


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Batch Bayesian Optimization via Local Penalization

González, J., Dai, Z., Hennig, P., Lawrence, N.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), May 2016 (conference)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Communication Rate Analysis for Event-based State Estimation

(Best student paper finalist)

Ebner, S., Trimpe, S.

In Proceedings of the 13th International Workshop on Discrete Event Systems, May 2016 (inproceedings)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Probabilistic Approximate Least-Squares

Bartels, S., Hennig, P.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 676-684, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C. ), May 2016 (conference)

Abstract
Least-squares and kernel-ridge / Gaussian process regression are among the foundational algorithms of statistics and machine learning. Famously, the worst-case cost of exact nonparametric regression grows cubically with the data-set size; but a growing number of approximations have been developed that estimate good solutions at lower cost. These algorithms typically return point estimators, without measures of uncertainty. Leveraging recent results casting elementary linear algebra operations as probabilistic inference, we propose a new approximate method for nonparametric least-squares that affords a probabilistic uncertainty estimate over the error between the approximate and exact least-squares solution (this is not the same as the posterior variance of the associated Gaussian process regressor). This allows estimating the error of the least-squares solution on a subset of the data relative to the full-data solution. The uncertainty can be used to control the computational effort invested in the approximation. Our algorithm has linear cost in the data-set size, and a simple formal form, so that it can be implemented with a few lines of code in programming languages with linear algebra functionality.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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Supplemental material for ’Communication Rate Analysis for Event-based State Estimation’

Ebner, S., Trimpe, S.

Max Planck Institute for Intelligent Systems, January 2016 (techreport)

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PDF [BibTex]

PDF [BibTex]


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Gaussian Process-Based Predictive Control for Periodic Error Correction

Klenske, E. D., Zeilinger, M., Schölkopf, B., Hennig, P.

IEEE Transactions on Control Systems Technology , 24(1):110-121, 2016 (article)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Dual Control for Approximate Bayesian Reinforcement Learning

Klenske, E. D., Hennig, P.

Journal of Machine Learning Research, 17(127):1-30, 2016 (article)

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Event-based Sampling for Reducing Communication Load in Realtime Human Motion Analysis by Wireless Inertial Sensor Networks

Laidig, D., Trimpe, S., Seel, T.

Current Directions in Biomedical Engineering, 2(1):711-714, De Gruyter, 2016 (article)

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PDF DOI [BibTex]

PDF DOI [BibTex]

2010


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Using an Infinite Von Mises-Fisher Mixture Model to Cluster Treatment Beam Directions in External Radiation Therapy

Bangert, M., Hennig, P., Oelfke, U.

In pages: 746-751 , (Editors: Draghici, S. , T.M. Khoshgoftaar, V. Palade, W. Pedrycz, M.A. Wani, X. Zhu), IEEE, Piscataway, NJ, USA, Ninth International Conference on Machine Learning and Applications (ICMLA), December 2010 (inproceedings)

Abstract
We present a method for fully automated selection of treatment beam ensembles for external radiation therapy. We reformulate the beam angle selection problem as a clustering problem of locally ideal beam orientations distributed on the unit sphere. For this purpose we construct an infinite mixture of von Mises-Fisher distributions, which is suited in general for density estimation from data on the D-dimensional sphere. Using a nonparametric Dirichlet process prior, our model infers probability distributions over both the number of clusters and their parameter values. We describe an efficient Markov chain Monte Carlo inference algorithm for posterior inference from experimental data in this model. The performance of the suggested beam angle selection framework is illustrated for one intra-cranial, pancreas, and prostate case each. The infinite von Mises-Fisher mixture model (iMFMM) creates between 18 and 32 clusters, depending on the patient anatomy. This suggests to use the iMFMM directly for beam ensemble selection in robotic radio surgery, or to generate low-dimensional input for both subsequent optimization of trajectories for arc therapy and beam ensemble selection for conventional radiation therapy.

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Web DOI [BibTex]

2010


Web DOI [BibTex]


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Coherent Inference on Optimal Play in Game Trees

Hennig, P., Stern, D., Graepel, T.

In JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010, pages: 326-333, (Editors: Teh, Y.W. , M. Titterington ), JMLR, Cambridge, MA, USA, Thirteenth International Conference on Artificial Intelligence and Statistics, May 2010 (inproceedings)

Abstract
Round-based games are an instance of discrete planning problems. Some of the best contemporary game tree search algorithms use random roll-outs as data. Relying on a good policy, they learn on-policy values by propagating information upwards in the tree, but not between sibling nodes. Here, we present a generative model and a corresponding approximate message passing scheme for inference on the optimal, off-policy value of nodes in smooth AND/OR trees, given random roll-outs. The crucial insight is that the distribution of values in game trees is not completely arbitrary. We define a generative model of the on-policy values using a latent score for each state, representing the value under the random roll-out policy. Inference on the values under the optimal policy separates into an inductive, pre-data step and a deductive, post-data part. Both can be solved approximately with Expectation Propagation, allowing off-policy value inference for any node in the (exponentially big) tree in linear time.

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PDF Web [BibTex]

PDF Web [BibTex]