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2019


Controlling Heterogeneous Stochastic Growth Processes on Lattices with Limited Resources
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) , pages: 1315-1322, 58th IEEE International Conference on Decision and Control (CDC), December 2019 (conference)

ics

PDF [BibTex]

2019


PDF [BibTex]


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Limitations of the empirical Fisher approximation for natural gradient descent

Kunstner, F., Hennig, P., Balles, L.

Advances in Neural Information Processing Systems 32, pages: 4158-4169, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

ei pn

link (url) [BibTex]

link (url) [BibTex]


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Convergence Guarantees for Adaptive Bayesian Quadrature Methods

Kanagawa, M., Hennig, P.

Advances in Neural Information Processing Systems 32, pages: 6234-6245, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

ei pn

link (url) [BibTex]

link (url) [BibTex]


A Learnable Safety Measure
A Learnable Safety Measure

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

Conference on Robot Learning, November 2019 (conference) Accepted

dlg ics

Arxiv [BibTex]

Arxiv [BibTex]


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

ics

arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]


Predictive Triggering for Distributed Control of Resource Constrained Multi-agent Systems
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, pages: 79-84, 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys), September 2019 (inproceedings)

ics

arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]


Event-triggered Pulse Control with Model Learning (if Necessary)
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 Project Page [BibTex]

arXiv PDF Project Page [BibTex]


Data-driven inference of passivity properties via Gaussian process optimization
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]


Trajectory-Based Off-Policy Deep Reinforcement Learning
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.

ics

arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Variational Autoencoders Recover PCA Directions (by Accident)

Rolinek, M., Zietlow, D., Martius, G.

In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2019, June 2019 (inproceedings)

Abstract
The Variational Autoencoder (VAE) is a powerful architecture capable of representation learning and generative modeling. When it comes to learning interpretable (disentangled) representations, VAE and its variants show unparalleled performance. However, the reasons for this are unclear, since a very particular alignment of the latent embedding is needed but the design of the VAE does not encourage it in any explicit way. We address this matter and offer the following explanation: the diagonal approximation in the encoder together with the inherent stochasticity force local orthogonality of the decoder. The local behavior of promoting both reconstruction and orthogonality matches closely how the PCA embedding is chosen. Alongside providing an intuitive understanding, we justify the statement with full theoretical analysis as well as with experiments.

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arXiv link (url) Project Page [BibTex]

arXiv link (url) Project Page [BibTex]


Resource-aware IoT Control: Saving Communication through Predictive Triggering
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.

ics

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)

ei pn

link (url) [BibTex]

link (url) [BibTex]


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

ei pn

PDF link (url) [BibTex]

PDF link (url) [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]


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

ei pn

PDF link (url) [BibTex]

PDF link (url) [BibTex]


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

Baumann, D.

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

ics

PDF [BibTex]

PDF [BibTex]


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Control What You Can: Intrinsically Motivated Task-Planning Agent

Blaes, S., Vlastelica, M., Zhu, J., Martius, G.

In Advances in Neural Information Processing (NeurIPS’19), pages: 12520-12531, Curran Associates, Inc., NeurIPS'19, 2019 (inproceedings)

Abstract
We present a novel intrinsically motivated agent that learns how to control the environment in the fastest possible manner by optimizing learning progress. It learns what can be controlled, how to allocate time and attention, and the relations between objects using surprise based motivation. The effectiveness of our method is demonstrated in a synthetic as well as a robotic manipulation environment yielding considerably improved performance and smaller sample complexity. In a nutshell, our work combines several task-level planning agent structures (backtracking search on task graph, probabilistic road-maps, allocation of search efforts) with intrinsic motivation to achieve learning from scratch.

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives
Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives

Gumbsch, C., Butz, M. V., Martius, G.

IEEE Transactions on Cognitive and Developmental Systems, 2019 (article)

Abstract
Voluntary behavior of humans appears to be composed of small, elementary building blocks or behavioral primitives. While this modular organization seems crucial for the learning of complex motor skills and the flexible adaption of behavior to new circumstances, the problem of learning meaningful, compositional abstractions from sensorimotor experiences remains an open challenge. Here, we introduce a computational learning architecture, termed surprise-based behavioral modularization into event-predictive structures (SUBMODES), that explores behavior and identifies the underlying behavioral units completely from scratch. The SUBMODES architecture bootstraps sensorimotor exploration using a self-organizing neural controller. While exploring the behavioral capabilities of its own body, the system learns modular structures that predict the sensorimotor dynamics and generate the associated behavior. In line with recent theories of event perception, the system uses unexpected prediction error signals, i.e., surprise, to detect transitions between successive behavioral primitives. We show that, when applied to two robotic systems with completely different body kinematics, the system manages to learn a variety of complex behavioral primitives. Moreover, after initial self-exploration the system can use its learned predictive models progressively more effectively for invoking model predictive planning and goal-directed control in different tasks and environments.

al

arXiv PDF video link (url) DOI Project Page [BibTex]


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Machine Learning for Haptics: Inferring Multi-Contact Stimulation From Sparse Sensor Configuration

Sun, H., Martius, G.

Frontiers in Neurorobotics, 13, pages: 51, 2019 (article)

Abstract
Robust haptic sensation systems are essential for obtaining dexterous robots. Currently, we have solutions for small surface areas such as fingers, but affordable and robust techniques for covering large areas of an arbitrary 3D surface are still missing. Here, we introduce a general machine learning framework to infer multi-contact haptic forces on a 3D robot’s limb surface from internal deformation measured by only a few physical sensors. The general idea of this framework is to predict first the whole surface deformation pattern from the sparsely placed sensors and then to infer number, locations and force magnitudes of unknown contact points. We show how this can be done even if training data can only be obtained for single-contact points using transfer learning at the example of a modified limb of the Poppy robot. With only 10 strain-gauge sensors we obtain a high accuracy also for multiple-contact points. The method can be applied to arbitrarily shaped surfaces and physical sensor types, as long as training data can be obtained.

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link (url) DOI [BibTex]


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Falsification of hybrid systems using symbolic reachability and trajectory splicing

Bogomolov, S., Frehse, G., Gurung, A., Li, D., Martius, G., Ray, R.

In International Conference on Hybrid Systems: Computation and Control, pages: 1-10, HSCC’19, ACM, 2019 (inproceedings)

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DOI [BibTex]

DOI [BibTex]


Probabilistic Linear Solvers: A Unifying View
Probabilistic Linear Solvers: A Unifying View

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

Statistics and Computing, 2019 (article) Accepted

pn

link (url) [BibTex]

link (url) [BibTex]


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Actively Learning Dynamical Systems with Gaussian Processes

Buisson-Fenet, M.

Mines ParisTech, PSL 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.

ics

[BibTex]

[BibTex]

2018


Deep Reinforcement Learning for Event-Triggered Control
Deep Reinforcement Learning for Event-Triggered Control

Baumann, D., Zhu, J., Martius, G., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 943-950, 57th IEEE International Conference on Decision and Control (CDC), December 2018 (inproceedings)

al ics

arXiv PDF DOI Project Page Project Page [BibTex]

2018


arXiv PDF DOI Project Page Project Page [BibTex]


Efficient Encoding of Dynamical Systems through Local Approximations
Efficient Encoding of Dynamical Systems through Local Approximations

Solowjow, F., Mehrjou, A., Schölkopf, B., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 6073 - 6079 , Miami, Fl, USA, December 2018 (inproceedings)

ei ics

arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


Depth Control of Underwater Robots using Sliding Modes and Gaussian Process Regression
Depth Control of Underwater Robots using Sliding Modes and Gaussian Process Regression

Lima, G. S., Bessa, W. M., Trimpe, S.

In Proceeding of the 15th Latin American Robotics Symposium, João Pessoa, Brazil, 15th Latin American Robotics Symposium, November 2018 (inproceedings)

Abstract
The development of accurate control systems for underwater robotic vehicles relies on the adequate compensation for hydrodynamic effects. In this work, a new robust control scheme is presented for remotely operated underwater vehicles. In order to meet both robustness and tracking requirements, sliding mode control is combined with Gaussian process regression. The convergence properties of the closed-loop signals are analytically proven. Numerical results confirm the stronger improved performance of the proposed control scheme.

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[BibTex]

[BibTex]


Gait learning for soft microrobots controlled by light fields
Gait learning for soft microrobots controlled by light fields

Rohr, A. V., Trimpe, S., Marco, A., Fischer, P., Palagi, S.

In International Conference on Intelligent Robots and Systems (IROS) 2018, pages: 6199-6206, International Conference on Intelligent Robots and Systems 2018, October 2018 (inproceedings)

Abstract
Soft microrobots based on photoresponsive materials and controlled by light fields can generate a variety of different gaits. This inherent flexibility can be exploited to maximize their locomotion performance in a given environment and used to adapt them to changing environments. However, because of the lack of accurate locomotion models, and given the intrinsic variability among microrobots, analytical control design is not possible. Common data-driven approaches, on the other hand, require running prohibitive numbers of experiments and lead to very sample-specific results. Here we propose a probabilistic learning approach for light-controlled soft microrobots based on Bayesian Optimization (BO) and Gaussian Processes (GPs). The proposed approach results in a learning scheme that is highly data-efficient, enabling gait optimization with a limited experimental budget, and robust against differences among microrobot samples. These features are obtained by designing the learning scheme through the comparison of different GP priors and BO settings on a semisynthetic data set. The developed learning scheme is validated in microrobot experiments, resulting in a 115% improvement in a microrobot’s locomotion performance with an experimental budget of only 20 tests. These encouraging results lead the way toward self-adaptive microrobotic systems based on lightcontrolled soft microrobots and probabilistic learning control.

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arXiv IEEE Xplore DOI Project Page [BibTex]

arXiv IEEE Xplore DOI Project Page [BibTex]


Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

pn

link (url) Project Page [BibTex]


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Learning-Based Robust Model Predictive Control with State-Dependent Uncertainty

Soloperto, R., Müller, M. A., Trimpe, S., Allgöwer, F.

In Proceedings of the IFAC Conference on Nonlinear Model Predictive Control (NMPC), Madison, Wisconsin, USA, 6th IFAC Conference on Nonlinear Model Predictive Control, August 2018 (inproceedings)

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PDF [BibTex]

PDF [BibTex]


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Kernel Recursive ABC: Point Estimation with Intractable Likelihood

Kajihara, T., Kanagawa, M., Yamazaki, K., Fukumizu, K.

Proceedings of the 35th International Conference on Machine Learning, pages: 2405-2414, PMLR, July 2018 (conference)

Abstract
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.

pn

Paper [BibTex]

Paper [BibTex]


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Learning an Approximate Model Predictive Controller with Guarantees

Hertneck, M., Koehler, J., Trimpe, S., Allgöwer, F.

IEEE Control Systems Letters, 2(3):543-548, July 2018 (article)

Abstract
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding’s Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

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arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]


Probabilistic Recurrent State-Space Models
Probabilistic Recurrent State-Space Models

Doerr, A., Daniel, C., Schiegg, M., Nguyen-Tuong, D., Schaal, S., Toussaint, M., Trimpe, S.

In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), July 2018 (inproceedings)

Abstract
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g., LSTMs) proved extremely successful in modeling complex time-series data. Fully probabilistic SSMs, however, unfortunately often prove hard to train, even for smaller problems. To overcome this limitation, we propose a scalable initialization and training algorithm based on doubly stochastic variational inference and Gaussian processes. In the variational approximation we propose in contrast to related approaches to fully capture the latent state temporal correlations to allow for robust training.

am ics

arXiv pdf Project Page [BibTex]

arXiv pdf Project Page [BibTex]


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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Event-triggered Learning for Resource-efficient Networked Control
Event-triggered Learning for Resource-efficient Networked Control

Solowjow, F., Baumann, D., Garcke, J., Trimpe, S.

In Proceedings of the American Control Conference (ACC), pages: 6506 - 6512, American Control Conference, June 2018 (inproceedings)

ics

arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Nonlinear decoding of a complex movie from the mammalian retina

Botella-Soler, V., Deny, S., Martius, G., Marre, O., Tkačik, G.

PLOS Computational Biology, 14(5):1-27, Public Library of Science, May 2018 (article)

Abstract
Author summary Neurons in the retina transform patterns of incoming light into sequences of neural spikes. We recorded from ∼100 neurons in the rat retina while it was stimulated with a complex movie. Using machine learning regression methods, we fit decoders to reconstruct the movie shown from the retinal output. We demonstrated that retinal code can only be read out with a low error if decoders make use of correlations between successive spikes emitted by individual neurons. These correlations can be used to ignore spontaneous spiking that would, otherwise, cause even the best linear decoders to “hallucinate” nonexistent stimuli. This work represents the first high resolution single-trial full movie reconstruction and suggests a new paradigm for separating spontaneous from stimulus-driven neural activity.

al

DOI [BibTex]

DOI [BibTex]


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Poster Abstract: Toward Fast Closed-loop Control over Multi-hop Low-power Wireless Networks

Mager, F., Baumann, D., Trimpe, S., Zimmerling, M.

Proceedings of the 17th ACM/IEEE Conference on Information Processing in Sensor Networks (IPSN), pages: 158-159, Porto, Portugal, April 2018 (poster)

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


Evaluating Low-Power Wireless Cyber-Physical Systems
Evaluating Low-Power Wireless Cyber-Physical Systems

Baumann, D., Mager, F., Singh, H., Zimmerling, M., Trimpe, S.

In Proceedings of the IEEE Workshop on Benchmarking Cyber-Physical Networks and Systems (CPSBench), pages: 13-18, IEEE Workshop on Benchmarking Cyber-Physical Networks and Systems (CPSBench), April 2018 (inproceedings)

ics

arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Distributed Event-Based State Estimation for Networked Systems: An LMI Approach

Muehlebach, M., Trimpe, S.

IEEE Transactions on Automatic Control, 63(1):269-276, January 2018 (article)

am ics

arXiv (extended version) DOI Project Page [BibTex]

arXiv (extended version) DOI Project Page [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

pn

arXiv [BibTex]

arXiv [BibTex]


Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients
Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients

Balles, L., Hennig, P.

In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018 (inproceedings) Accepted

Abstract
The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of stochastic gradients, whereas the update magnitude is determined by an estimate of their relative variance. We disentangle these two aspects and analyze them in isolation, gaining insight into the mechanisms underlying ADAM. This analysis also extends recent results on adverse effects of ADAM on generalization, isolating the sign aspect as the problematic one. Transferring the variance adaptation to SGD gives rise to a novel method, completing the practitioner's toolbox for problems where ADAM fails.

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

ei pn

arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

arXiv [BibTex]


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L4: Practical loss-based stepsize adaptation for deep learning

Rolinek, M., Martius, G.

In Advances in Neural Information Processing Systems 31 (NeurIPS 2018), pages: 6434-6444, (Editors: S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett), Curran Associates, Inc., 2018 (inproceedings)

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Github link (url) Project Page [BibTex]

Github link (url) Project Page [BibTex]


A probabilistic model for the numerical solution of initial value problems
A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

pn

PDF Code DOI Project Page [BibTex]


Systematic self-exploration of behaviors for robots in a dynamical systems framework
Systematic self-exploration of behaviors for robots in a dynamical systems framework

Pinneri, C., Martius, G.

In Proc. Artificial Life XI, pages: 319-326, MIT Press, Cambridge, MA, 2018 (inproceedings)

Abstract
One of the challenges of this century is to understand the neural mechanisms behind cognitive control and learning. Recent investigations propose biologically plausible synaptic mechanisms for self-organizing controllers, in the spirit of Hebbian learning. In particular, differential extrinsic plasticity (DEP) [Der and Martius, PNAS 2015], has proven to enable embodied agents to self-organize their individual sensorimotor development, and generate highly coordinated behaviors during their interaction with the environment. These behaviors are attractors of a dynamical system. In this paper, we use the DEP rule to generate attractors and we combine it with a “repelling potential” which allows the system to actively explore all its attractor behaviors in a systematic way. With a view to a self-determined exploration of goal-free behaviors, our framework enables switching between different motion patterns in an autonomous and sequential fashion. Our algorithm is able to recover all the attractor behaviors in a toy system and it is also effective in two simulated environments. A spherical robot discovers all its major rolling modes and a hexapod robot learns to locomote in 50 different ways in 30min.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Probabilistic Approaches to Stochastic Optimization

Mahsereci, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

ei pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Learning equations for extrapolation and control
Learning equations for extrapolation and control

Sahoo, S. S., Lampert, C. H., Martius, G.

In Proc. 35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, 2018, 80, pages: 4442-4450, http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf, (Editors: Dy, Jennifer and Krause, Andreas), PMLR, 2018 (inproceedings)

Abstract
We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

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Code Arxiv Poster Slides link (url) Project Page [BibTex]

Code Arxiv Poster Slides link (url) Project Page [BibTex]