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6 results (BibTeX)

2015


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Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

In Advances in Neural Information Processing Systems 28, pages: 181-189, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (inproceedings)

Abstract
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent. [You can find the matlab research code under `attachments' below. The zip-file contains a minimal working example. The docstring in probLineSearch.m contains additional information. A more polished implementation in C++ will be published here at a later point. For comments and questions about the code please write to mmahsereci@tue.mpg.de.]

Matlab research code link (url) Project Page [BibTex]

2015

Matlab research code link (url) Project Page [BibTex]


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Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results

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

Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems, September 2015 (conference)

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. Preliminary results of a low-dimensional tuning problem highlight the method’s potential for automatic controller tuning on robotic platforms.

PDF Project Page [BibTex]

PDF Project Page [BibTex]


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Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

Hauberg, S., Schober, M., Liptrot, M., Hennig, P., Feragen, A.

In 18th International Conference on Medical Image Computing and Computer Assisted Intervention, 9349, pages: 597-604, Lecture Notes in Computer Science, MICCAI, 2015 (inproceedings)

PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Inference of Cause and Effect with Unsupervised Inverse Regression

Sgouritsa, E., Janzing, D., Hennig, P., Schölkopf, B.

In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, 38, pages: 847-855, JMLR Workshop and Conference Proceedings, (Editors: Lebanon, G. and Vishwanathan, S.V.N.), JMLR.org, AISTATS, 2015 (inproceedings)

Web PDF Project Page [BibTex]

Web PDF Project Page [BibTex]